Data Science Homework - Homework assignment for Data Scientist candidate

Loading the needed libraries and setting the working directory
library(tidyverse)
-- Attaching packages --------------------------------------- tidyverse 1.2.1 --
v ggplot2 2.2.1     v purrr   0.2.5
v tibble  1.4.2     v dplyr   0.7.5
v tidyr   0.8.1     v stringr 1.3.1
v readr   1.1.1     v forcats 0.3.0
-- Conflicts ------------------------------------------ tidyverse_conflicts() --
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
library(lubridate)

Attaching package: <U+393C><U+3E31>lubridate<U+393C><U+3E32>

The following object is masked from <U+393C><U+3E31>package:base<U+393C><U+3E32>:

    date
Importing the data from the zip file
order <- read.table(unz("data.zip", "order.csv"), header=T, quote="\"", sep=",")
online<- read.table(unz("data.zip", "online.csv"), header=T, quote="\"", sep=",")

1. Exploration and understanding of the data sets

Order dataset

Lets look at the structure of the data

str(order)
'data.frame':   263278 obs. of  6 variables:
 $ custno   : int  18944 18944 18944 36096 1 6401 25601 57601 2 2 ...
 $ ordno    : int  64694 114405 28906 62681 1 8187 41198 112311 2 70848 ...
 $ orderdate: Factor w/ 149482 levels "2016-01-01 05:05:14",..: 44835 68024 67301 7798 75039 63162 88311 58274 12156 4041 ...
 $ prodcat2 : int  NA NA NA NA NA NA NA NA NA NA ...
 $ prodcat1 : int  1 1 1 1 1 1 1 1 1 1 ...
 $ revenue  : num  53.3 0.1 141.66 36.82 8.35 ...

we can see that the custno, ordno, prodcat2, prodcat1 are integer but should be factors. Also, orderdate is a factor which should be a Datetime column. Changing the data type of these columns.

order[c('custno','ordno','prodcat1','prodcat2')] <- lapply(order[c('custno','ordno','prodcat1','prodcat2')], factor)  ## as.factor() could also be used
order$orderdate <- strptime(x = as.character(order$orderdate),
                                format = "%Y-%m-%d %H:%M:%S")
order$orderdate <- as.POSIXct(order$orderdate, tz = "", format="%Y-%m-%d %H:%M:%S")
str(order)
'data.frame':   263278 obs. of  6 variables:
 $ custno   : Factor w/ 70264 levels "1","2","3","4",..: 18898 18898 18898 35970 1 6382 25539 57238 2 2 ...
 $ ordno    : Factor w/ 149717 levels "1","2","3","4",..: 64382 113630 28757 62375 1 8123 41017 111562 2 70445 ...
 $ orderdate: POSIXct, format: "2016-11-27 20:57:20" "2017-04-29 20:18:04" "2017-04-23 21:31:03" "2016-02-25 07:16:33" ...
 $ prodcat2 : Factor w/ 251 levels "2","3","4","5",..: NA NA NA NA NA NA NA NA NA NA ...
 $ prodcat1 : Factor w/ 6 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ revenue  : num  53.3 0.1 141.66 36.82 8.35 ...

Now lets look at the summary of the data.

summary(order)
     custno           ordno          orderdate                      prodcat2      prodcat1     revenue      
 56     :   626   6076   :    26   Min.   :2016-01-01 05:05:14   3      : 40908   1:48672   Min.   :  0.00  
 2758   :   451   4803   :    21   1st Qu.:2016-09-28 11:22:56   4      : 15797   2:88684   1st Qu.: 37.43  
 2511   :   368   5207   :    20   Median :2017-06-25 08:56:10   13     : 13567   3:44019   Median : 74.93  
 1055   :   350   23233  :    19   Mean   :2017-06-29 11:35:41   16     : 13470   4:46681   Mean   : 74.94  
 709    :   345   28041  :    19   3rd Qu.:2018-03-25 09:39:11   11     : 13400   5:11180   3rd Qu.:112.28  
 3844   :   345   23907  :    17   Max.   :2019-01-02 23:54:58   (Other):164313   7:24042   Max.   :150.00  
 (Other):260793   (Other):263156                                 NA's   :  1823                             

We can see that we have the order data for years 2016, 2017, and 2018. We can also see that there are some missing values in prodcat2.

Lets explore at prodcat2

length(unique(order$prodcat2))
[1] 252

We have 252 levels in the prodcat2 categorical variable. Lets try to understand the mapping between prodcat1 and prodcat2

tab<-table(order$prodcat2,order$prodcat1)
head(tab,50)
    
         1     2     3     4     5     7
  2      0  5148     0     0     0     0
  3      0 40908     0     0     0     0
  4      0 15797     0     0     0     0
  5      0 12946     0     0     0     0
  6      0     0  5393     0     0     0
  7      0  2294     0     0     0     0
  8      0     0   133     0     0     0
  9      0     0 12671     0     0     0
  10     0   570     0     0     0     0
  11 13400     0     0     0     0     0
  12  1891     0     0     0     0     0
  13     0     0     0 13567     0     0
  14  4251     0     0     0     0     0
  15     0     0     0   730     0     0
  16     0     0     0 13470     0     0
  17     0     0     0     0   127     0
  18     0     0     0  2758     0     0
  19   926     0     0     0     0     0
  20     0     0     0     0  1081     0
  21   906     0     0     0     0     0
  23     0    30     0     0     0     0
  24   461     0     0     0     0     0
  25     0     0     0     0     0  4773
  26     0     0   266     0     0     0
  27     0     0  3535     0     0     0
  28     0     0     0     0     0  4785
  30     0     0  4217     0     0     0
  32     0     0   216     0     0     0
  33   303     0     0     0     0     0
  34    55     0     0     0     0     0
  35     0   735     0     0     0     0
  38     0     0     0     0  6552     0
  39     0     0     0     0  2321     0
  40  1344     0     0     0     0     0
  41  1156     0     0     0     0     0
  42     0  2282     0     0     0     0
  43     0     0  2400     0     0     0
  44     0     0  1647     0     0     0
  45     0     0  2357     0     0     0
  46     0   217     0     0     0     0
  47     0     0     0     0     0   208
  48     0     0   472     0     0     0
  49     0     0   279     0     0     0
  50     0     0     0     0     0  2493
  51     0     0   798     0     0     0
  52     0     0   182     0     0     0
  53     0     0    33     0     0     0
  54     0     0     0  1090     0     0
  55     0   138     0     0     0     0
  56     0     0    99     0     0     0

There are also NA’s in the prodcat2.

summary(order$prodcat2)
      3       4      13      16      11       5      89       9      78      38       6       2      28      25 
  40908   15797   13567   13470   13400   12946   12772   12671    8341    6552    5393    5148    4785    4773 
     14      30     110      27      96      18      58     119      50      43      45      39       7      42 
   4251    4217    3954    3535    3520    2758    2596    2572    2493    2400    2357    2321    2294    2282 
     59      12     107      44      77     145      75      40     147      41      54      20      85      99 
   2068    1891    1673    1647    1604    1457    1448    1344    1340    1156    1090    1081     960     960 
     19     213      21      51      70      93      35      15      69     131      74     155      97      10 
    926     922     906     798     766     745     735     730     726     711     656     584     577     570 
    116      80      48     115      24     180     149     169      67     113     168     195     132      91 
    522     511     472     470     461     451     444     425     385     384     374     356     341     324 
     33      94     134      49      57      66     171      26     165     138      92     144      62      73 
    303     291     284     279     277     273     271     266     264     263     259     241     231     223 
    174      46     114      32      47      90     140      79      72     214      52     146     183     112 
    220     217     217     216     208     202     202     201     193     187     182     180     179     173 
(Other)    NA's 
   6889    1823 

There are 1823 NA’s in the prodcat2 field. We could impute these values using statistical methods. However, given the time-constraint, we won’t dive deep into prodcat2.

Lets first understand the level of the data. Intuitively, it looks like that the data is at product level. Lets check that by aggregating data.

level_ord<- order %>% group_by(custno,ordno,orderdate,prodcat1,prodcat2) %>% summarise(cnt=n()) %>% arrange(desc(cnt))
head(level_ord)

We can see that for custno 9 and ordno 23204, we are getting the cnt of more than 1 for each combination of prodcat1 and prodcat2. Lets look at the order data for this case

order %>% filter(custno==9,ordno==23204)
  custno ordno           orderdate prodcat2 prodcat1 revenue
1      9 23204 2016-01-03 18:27:48        3        2    1.27
2      9 23204 2016-01-03 18:27:48        3        2   33.11
3      9 23204 2016-01-03 18:27:48      110        2   90.07
4      9 23204 2016-01-03 18:27:48      110        2  131.97

We clearly see from the above example that the data is at product level. Lets get it at order and prodcat1 level.

order_agg<- order %>% group_by(custno,ordno,orderdate,prodcat1) %>% summarise(revenue = sum(revenue), num_prod = n())
head(order_agg,10)

Lets look at revenue.

summary(order$revenue)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   0.00   37.43   74.93   74.94  112.28  150.00 
hist(order$revenue,breaks = 30)

We can see from the histogram that revenue is uniformly distributed. Lets check revenue and ordersize across different prodcat1 and customers

order %>% group_by(prodcat1) %>% summarise(avg_rev_per_product=mean(revenue),total_rev=sum(revenue),num_orders=length(unique(ordno)),cnt_cust=length(unique(custno)))
# A tibble: 6 x 5
  prodcat1 avg_rev_per_product total_rev num_orders cnt_cust
  <fct>                  <dbl>     <dbl>      <int>    <int>
1 1                       74.9  3644599.      29875    18241
2 2                       75.2  6669793.      53510    30260
3 3                       74.7  3290307.      36538    17614
4 4                       74.7  3484911.      28188    17775
5 5                       75.7   846064.       9724     4684
6 7                       74.6  1794195.      21669    10670

From the above data we can see that the prodcat1=1 has the highest sales volume both in terms of revenue, number of orders as well as number of customers, whereas prodcat1=5 has the lowest.

Lets look at trend in revenue with time

library(lubridate)
order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue)) + geom_bar(stat='identity')+
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")

We can see a seasonlaity here. The Revenue peaks during the months of Dec and Jan. It then drops during the month of Feb and starts rising again and reaches another peak around May-June and then plunges in Oct. Then it rises again and peaks in Dec-Jan. The highest revenue was earned in Jan-2017 and lowest in Oct-2018.Lets break it down across product category and see if we get any seasonality across prodcat1.

order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month,prodcat1) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue,color=prodcat1,group=prodcat1)) +                    geom_line()+ facet_wrap(~prodcat1,nrow=3, scales = 'free') +
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")

We can see a seasonality across all the prodcat1 similar to the overall revenue category

We expect a similar trend for num_products ordered. Lets calculate the correlation between revenue and number of products ordered.

cor(order_agg$revenue,order_agg$num_prod)
[1] 0.7414783

The two fields are highly correlated which is evident from the scatter-plot given below

order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()

Lets look at the scatterplot across each product category and calculate the correlation at that level.

order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()+ facet_wrap(~prodcat1,nrow=3, scales = 'free')

order_agg %>% group_by(prodcat1) %>% summarise(cor_rev_prod=cor(revenue,num_prod))
# A tibble: 6 x 2
  prodcat1 cor_rev_prod
  <fct>           <dbl>
1 1               0.710
2 2               0.796
3 3               0.642
4 4               0.690
5 5               0.531
6 7               0.557

The correlation across each prodcat1 is high.

Online dataset

Lets look at the structure of the data

str(online)
'data.frame':   954774 obs. of  7 variables:
 $ session : int  419542 3030130 2638740 880408 2612179 880953 418956 281663 26191 1363670 ...
 $ visitor : int  140970 14501 419353 90673 191542 419268 14938 419163 419163 14464 ...
 $ dt      : Factor w/ 942579 levels "2016-01-01 00:00:08",..: 302552 854890 652906 833133 156326 222492 891922 466197 367097 644408 ...
 $ custno  : int  3840 70400 21248 39168 47616 47616 47872 49920 49920 54784 ...
 $ category: int  1 1 1 1 1 1 1 1 1 1 ...
 $ event1  : int  NA NA NA NA NA NA NA NA NA NA ...
 $ event2  : int  1 1 1 1 1 1 1 1 1 1 ...

The categorical columns custno, category, event1, event2, session, and visitor are in integer and the dt column should be of datetime datetype.

online[c('session','visitor','custno','category','event1','event2')] <- lapply(online[c('session','visitor','custno','category','event1','event2')], factor)  ## as.factor() could also be used
online$dt <- strptime(x = as.character(online$dt),
                                format = "%Y-%m-%d %H:%M:%S")
online$dt <- as.POSIXct(online$dt, tz = "", format="%Y-%m-%d %H:%M:%S")
str(online)
'data.frame':   954774 obs. of  7 variables:
 $ session : Factor w/ 850235 levels "2","3","6","9",..: 93667 680561 591950 197824 586838 197906 93569 62818 6501 307342 ...
 $ visitor : Factor w/ 259950 levels "1","3","5","6",..: 73857 9086 217101 48286 99883 217040 9388 216958 216958 9058 ...
 $ dt      : POSIXct, format: "2016-09-16 05:03:23" "2017-11-13 04:58:12" "2017-05-24 16:10:38" "2017-10-28 13:42:38" ...
 $ custno  : Factor w/ 57584 levels "6","7","8","9",..: 3173 56713 17326 31495 38364 38364 38560 40169 40169 43840 ...
 $ category: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
 $ event1  : Factor w/ 10 levels "1","2","4","5",..: NA NA NA NA NA NA NA NA NA NA ...
 $ event2  : Factor w/ 10 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...

Lets look at the summary of the data

summary(online)
    session          visitor             dt                          custno       category       event1      
 72733  :     5   328620 :   440   Min.   :2016-01-01 00:00:08   713    :   855   1: 52964   1      : 51567  
 157423 :     5   178635 :   310   1st Qu.:2016-07-25 15:01:06   10785  :   505   2:194890   4      : 23858  
 161973 :     5   227902 :   281   Median :2016-12-27 07:21:38   34515  :   479   3:706920   2      : 23312  
 692928 :     5   53505  :   276   Mean   :2017-01-10 19:15:08   336    :   473              11     : 20586  
 811699 :     5   279881 :   276   3rd Qu.:2017-07-10 18:51:39   28702  :   470              6      : 16537  
 1178030:     5   328827 :   254   Max.   :2017-12-31 23:58:05   57148  :   425              (Other): 29068  
 (Other):954744   (Other):952937                                 (Other):951567              NA's   :789846  
     event2      
 7      :367857  
 3      :129795  
 8      :122402  
 4      : 94230  
 1      : 86496  
 9      : 52145  
 (Other):101849  

We can see that the duration of the online data is from Jan-2016 to Dec-2017. We have 3 levels in online browsing category and multiple levels in event1 and event2. Lets first compare the number of customers in online vs order.

length(unique(online$custno))
[1] 57584
length(unique(order$custno))
[1] 70264

There are 57584 customers in online and 70264 customers in the order dataset. Getting a list of customers common to both the datasets

common_cust<-unique(order[which(order$custno %in% unique(online$custno)),]$custno)
length(common_cust)
[1] 56764

Lets calculate online activity across each of online browsing categories.

online %>% group_by(category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))
# A tibble: 3 x 4
  category activity unique_sessions num_cust
  <fct>       <int>           <int>    <int>
1 1           52964           47228    10001
2 2          194890          175809    30466
3 3          706920          627275    51222

Here activity means any sort of activity, be it creation of session, change in event1 or event2 etc. Unique sessions is the count of unique sessions created on each category and new_cust is the number of unique customers that used that category. Here, online browsing category could mean which device or what channel is used by the customer to browse the website.

Moving onto event1, we can see that majority of the values in that field are null

prop.table(table(online$event1,useNA = "ifany"))*100

         1          2          4          5          6          7          8          9         10         11 
 5.4009640  2.4416249  2.4988112  0.1542773  1.7320329  1.1956756  1.1485441  0.4178999  0.1280931  2.1561123 
      <NA> 
82.7259645 

83% of the values are null in event1. We will assume here that all the null values in event1 belong to one class which is class 0.

levels(online$event1)
 [1] "1"  "2"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11"
online$event1<-factor(ifelse(is.na(online$event1), 0, paste(online$event1)), levels = c(levels(online$event1), 0))
levels(online$event1)
 [1] "1"  "2"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "0" 
prop.table(table(online$event1))*100

         1          2          4          5          6          7          8          9         10         11 
 5.4009640  2.4416249  2.4988112  0.1542773  1.7320329  1.1956756  1.1485441  0.4178999  0.1280931  2.1561123 
         0 
82.7259645 

Lets look at event2,

prop.table(table(online$event2,useNA = "ifany"))*100

         1          2          3          4          5          6          7          8          9         10 
 9.0593167  1.6149371 13.5943166  9.8693513  5.0569035  3.1329927 38.5281753 12.8199972  5.4615019  0.8625078 

We can see that event2 is a highly imbalanced class with 39% of the data is in class 7 and 14% in class3. Lets look at online activity across each of the class in event2.

online %>% group_by(event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))
# A tibble: 10 x 4
   event2 activity unique_sessions num_cust
   <fct>     <int>           <int>    <int>
 1 1         86496           86496    28945
 2 2         15419           15175     9607
 3 3        129795          129788    34495
 4 4         94230           94123    32906
 5 5         48282           48023    21858
 6 6         29913           29873    14487
 7 7        367857          355901    50696
 8 8        122402          122388    36507
 9 9         52145           52144    24552
10 10         8235            8057     3985

AS expected, most of the activity is across class7 followed by class3 and class8. However, its still not enough to tell us what the value of each those class means.

Lets look at the time series trends of online activity

online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+ theme(axis.text.x = element_text(angle = 90, hjust = 1))

We will further break it down by browsing category

online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~category, nrow=2,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))

Lets break down online activity by event2.

online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~event2, nrow=5,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))

From all the online activity plot, we can see a seasonality trend. The online activity starts peaking from Nov till Jan then falls to the lowest in Feb. It then remains pretty steady till Oct. This trend is similar to the one we obtained for revenue and number of orders.

2.Feature engineering

Lets try to understand the level of the data in online dataset.

level_online<-online %>% group_by(session,custno,dt,event1,event2)%>% summarise(cnt=n()) %>% arrange(desc(cnt)) 
head(level_online)

We can see that each record is uniquely identified at session, customer, datetime, event1, and event2. Lets change the level of the data by spreading the online data on event2

online$val<-1
online_spread_e2<-spread(online,event2,val,fill=0,sep = '_')
head(online_spread_e2)
  session visitor                  dt custno category event1 event2_1 event2_2 event2_3 event2_4 event2_5 event2_6
1  419542  140970 2016-09-16 05:03:23   3840        1      0        1        0        0        0        0        0
2 3030130   14501 2017-11-13 04:58:12  70400        1      0        1        0        0        0        0        0
3 2638740  419353 2017-05-24 16:10:38  21248        1      0        1        0        0        0        0        0
4  880408   90673 2017-10-28 13:42:38  39168        1      0        1        0        0        0        0        0
5 2612179  191542 2016-05-17 06:30:32  47616        1      0        1        0        0        0        0        0
6  880953  419268 2016-07-15 12:36:42  47616        1      0        1        0        0        0        0        0
  event2_7 event2_8 event2_9 event2_10
1        0        0        0         0
2        0        0        0         0
3        0        0        0         0
4        0        0        0         0
5        0        0        0         0
6        0        0        0         0
online$val<-NULL

We will further spread the online data on key event1.

online_spread_e2$val<-1
online_spread_e2e1<-spread(online_spread_e2,event1,val,fill=0,sep = '_')
head(online_spread_e2e1)
  session visitor                  dt custno category event2_1 event2_2 event2_3 event2_4 event2_5 event2_6 event2_7
1  419542  140970 2016-09-16 05:03:23   3840        1        1        0        0        0        0        0        0
2 3030130   14501 2017-11-13 04:58:12  70400        1        1        0        0        0        0        0        0
3 2638740  419353 2017-05-24 16:10:38  21248        1        1        0        0        0        0        0        0
4  880408   90673 2017-10-28 13:42:38  39168        1        1        0        0        0        0        0        0
5 2612179  191542 2016-05-17 06:30:32  47616        1        1        0        0        0        0        0        0
6  880953  419268 2016-07-15 12:36:42  47616        1        1        0        0        0        0        0        0
  event2_8 event2_9 event2_10 event1_1 event1_2 event1_4 event1_5 event1_6 event1_7 event1_8 event1_9 event1_10
1        0        0         0        0        0        0        0        0        0        0        0         0
2        0        0         0        0        0        0        0        0        0        0        0         0
3        0        0         0        0        0        0        0        0        0        0        0         0
4        0        0         0        0        0        0        0        0        0        0        0         0
5        0        0         0        0        0        0        0        0        0        0        0         0
6        0        0         0        0        0        0        0        0        0        0        0         0
  event1_11 event1_0
1         0        1
2         0        1
3         0        1
4         0        1
5         0        1
6         0        1

There is also a possibility that a customer can use different browsing categories (for example, custno 6). To account for that we have to spread the data by category as well.

online_spread_e2e1$val<-1
online_spread_e2e1cat<-spread(online_spread_e2e1,category,val,fill=0,sep = '_')
head(online_spread_e2e1cat)
  session visitor                  dt custno event2_1 event2_2 event2_3 event2_4 event2_5 event2_6 event2_7 event2_8
1  419542  140970 2016-09-16 05:03:23   3840        1        0        0        0        0        0        0        0
2 3030130   14501 2017-11-13 04:58:12  70400        1        0        0        0        0        0        0        0
3 2638740  419353 2017-05-24 16:10:38  21248        1        0        0        0        0        0        0        0
4  880408   90673 2017-10-28 13:42:38  39168        1        0        0        0        0        0        0        0
5 2612179  191542 2016-05-17 06:30:32  47616        1        0        0        0        0        0        0        0
6  880953  419268 2016-07-15 12:36:42  47616        1        0        0        0        0        0        0        0
  event2_9 event2_10 event1_1 event1_2 event1_4 event1_5 event1_6 event1_7 event1_8 event1_9 event1_10 event1_11
1        0         0        0        0        0        0        0        0        0        0         0         0
2        0         0        0        0        0        0        0        0        0        0         0         0
3        0         0        0        0        0        0        0        0        0        0         0         0
4        0         0        0        0        0        0        0        0        0        0         0         0
5        0         0        0        0        0        0        0        0        0        0         0         0
6        0         0        0        0        0        0        0        0        0        0         0         0
  event1_0 category_1 category_2 category_3
1        1          1          0          0
2        1          1          0          0
3        1          1          0          0
4        1          1          0          0
5        1          1          0          0
6        1          1          0          0

Now, we will engineer features from Order data. One set of important features are is the revenue made by a customer on the last order of the same product category as well as and the number number of items ordered the last time. I have created those features below

order_agg<- order_agg %>% arrange(custno,prodcat1,orderdate,) %>% group_by(custno, prodcat1) %>% mutate(cum_rev=cumsum(revenue), cum_num_prod=cumsum(num_prod))
order_agg$cumrev_till_prev_order <- order_agg$cum_rev - order_agg$revenue
order_agg$cumnum_prod_till_prev_order <- order_agg$cum_num_prod - order_agg$num_prod
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
  group_by(custno,prodcat1) %>%
  mutate(rev_prev_ord = dplyr::lag(revenue, n = 1, default = 0),num_prod_prev_ord = dplyr::lag(num_prod, n = 1, default = 0))
order_agg[,c("revenue","num_prod","cum_rev","cum_num_prod")]<-NULL
summary(order_agg)
     custno           ordno          orderdate                   prodcat1  cumrev_till_prev_order
 56     :   479   1974   :     5   Min.   :2016-01-01 05:05:14   1:29875   Min.   :    0.0       
 2758   :   347   2794   :     5   1st Qu.:2016-09-25 19:15:03   2:53510   1st Qu.:    0.0       
 1055   :   321   3657   :     5   Median :2017-06-17 17:01:47   3:36538   Median :    0.0       
 1488   :   303   4577   :     5   Mean   :2017-06-24 14:26:40   4:28188   Mean   :  445.5       
 1581   :   269   5614   :     5   3rd Qu.:2018-03-17 07:09:34   5: 9724   3rd Qu.:  387.6       
 3844   :   268   5949   :     5   Max.   :2019-01-02 23:54:58   7:21669   Max.   :22676.0       
 (Other):177517   (Other):179474                                                                 
 cumnum_prod_till_prev_order  rev_prev_ord     num_prod_prev_ord
 Min.   :  0.000             Min.   :   0.00   Min.   : 0.0000  
 1st Qu.:  0.000             1st Qu.:   0.00   1st Qu.: 0.0000  
 Median :  0.000             Median :   0.00   Median : 0.0000  
 Mean   :  5.976             Mean   :  45.24   Mean   : 0.6045  
 3rd Qu.:  5.000             3rd Qu.:  83.79   3rd Qu.: 1.0000  
 Max.   :305.000             Max.   :1578.89   Max.   :17.0000  
                                                                

The following four metrics are created. 1. cum_rev_till_prev_order: This is the cumulative revenue of a customer till previous order 2. cumnum_prod_till_prev_order: Cumulative number of items till previous order. 3. rev_prev_order: revenue made from previous order 4. num_prod_prev_order: Number of items ordered from previous order

Another important metric would be number of days till last order

order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
  group_by(custno,prodcat1) %>%
  mutate(orderdate_prev_ord = dplyr::lag(orderdate, n = 1, default = NA))
order_agg$num_days_till_last_order <- difftime(order_agg$orderdate, order_agg$orderdate_prev_ord, units="days")
order_agg$orderdate_prev_ord<-NULL
order_agg$num_days_till_last_order <-as.numeric(order_agg$num_days_till_last_order)
summary(order_agg$num_days_till_last_order)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
   0.00    9.65   35.19  100.02  127.97 1081.32   99244 

The order aggregate data now looks like.

head(order_agg,10)

Now lets join the above data with order_agg data (order data aggregated at order-prodcat1 level). We will join order_agg with prodcat1 on the inequality. Since we are planning to predict prodcat1, we will put order_agg on the left and perform a left join.

joined_df<-left_join(order_agg,online_spread_e2e1cat,by="custno") 
Column `custno` joining factors with different levels, coercing to character vector
joined_df[,13:36][is.na(joined_df[,13:36])] <- 0
joined_df$dt<- as.character(joined_df$dt)
joined_df$dt<-ifelse(joined_df$dt>joined_df$orderdate,NA,joined_df$dt)
joined_df$dt <- strptime(x = as.character(joined_df$dt),
                                format = "%Y-%m-%d %H:%M:%S")
joined_df$dt <- as.POSIXct(joined_df$dt, tz = "", format="%Y-%m-%d %H:%M:%S")
joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")]<-lapply(joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")], function(x) ifelse(is.na(joined_df$dt)==TRUE,NA,x))
joined_df<- joined_df %>% filter(orderdate>=dt | is.na(dt)==TRUE)
head(joined_df,20)

as you can see for a customer with a given orderno and prodcat1, only the online activity on or before the time of the order is joined. Now lets calculate the difference between orderdate and dt. Note: We are also incluing the order data for which no online data is available

joined_df$date_diff<- difftime(joined_df$orderdate,joined_df$dt,units = 'days')
head(joined_df,20)

We are assuming that only the last 30 days of online activity drives buying behaviour. Therefor we will only consider online activities and browsing category that occured 30 days before a transaction.

What we have done above is for date difference greater than 30 days, we have changed the events flags (event2_1, event2_2 etc.) and to browsing category flags to 0 as we are not considering those events to have an impact on the buying behaviour. Now we will aggregate the data by taking the count of each events and categories. This count will be the number of times that event has happened (or browsing category used) in the past 30 days before a transaction.

Now we will aggregate the data to order-prodcat1 level

df<- joined_df_new %>% group_by(custno,ordno,orderdate,prodcat1,cumrev_till_prev_order,cumnum_prod_till_prev_order,rev_prev_ord,num_prod_prev_ord,num_days_till_last_order) %>% 
  summarise(sum_category_1 = sum(category_1),
            sum_category_2 = sum(category_2),
            sum_category_3 = sum(category_3),
            sum_event1_1 = sum(event1_1),
            sum_event1_2 = sum(event1_2),
            sum_event1_4 = sum(event1_4),
            sum_event1_5 = sum(event1_5),
            sum_event1_6 = sum(event1_6),
            sum_event1_7 = sum(event1_7),
            sum_event1_8 = sum(event1_8),
            sum_event1_9 = sum(event1_9),
            sum_event1_10 = sum(event1_10),
            sum_event1_11 = sum(event1_11),
            sum_event2_1 = sum(event2_1),
            sum_event2_2 = sum(event2_2),
            sum_event2_3 = sum(event2_3),
            sum_event2_4 = sum(event2_4),
            sum_event2_5 = sum(event2_5),
            sum_event2_6 = sum(event2_6),
            sum_event2_7 = sum(event2_7),
            sum_event2_8 = sum(event2_8),
            sum_event2_9 = sum(event2_9),
            sum_event2_10 = sum(event2_10),
            avg_date_diff = mean(date_diff,na.rm = TRUE)
            )
head(df)

Another metric we can include is revenue per product for cumuative value as well as previous orders

df$cumrev_per_prod_till_prev_order <- ifelse(df$cumrev_till_prev_order==0,0,df$cumrev_till_prev_order/df$cumnum_prod_till_prev_order)
df$rev_per_prod_prev_ord <- ifelse(df$rev_prev_ord==0,0,df$rev_prev_ord/df$num_prod_prev_ord)
df[,c('cumrev_till_prev_order','cumnum_prod_till_prev_order','rev_prev_ord','num_prod_prev_ord')]<-NULL
df$avg_date_diff<-as.numeric(df$avg_date_diff)

Breaking down orderdate to month, quarter, day-of-week, week of the year and hour

df$order_month<-format(df$orderdate,"%m")
df$order_week_of_year<-strftime(df$orderdate,format="%W")
library(lubridate)
df$order_qtr<-quarter(df$orderdate)
df$order_day_of_week<-weekdays(df$orderdate,abbreviate = TRUE)
df$order_hour_of_day<-format(df$orderdate,"%H")
# converting the above features to factors
df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')] <- lapply(df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')], factor)

We have created the folllowing features by manipulating and combining order and online data.

head(df)
# A tibble: 6 x 36
  custno ordno orderdate           prodcat1 num_days_till_last_order sum_category_1 sum_category_2 sum_category_3
  <chr>  <fct> <dttm>              <fct>                       <dbl>          <dbl>          <dbl>          <dbl>
1 1      1     2017-06-12 08:27:59 1                             NA               0              0              0
2 10     10    2017-04-09 23:38:53 2                             NA               0              0              0
3 100    101   2017-11-22 04:52:43 1                            359.              0              0              0
4 100    101   2017-11-22 04:52:43 2                            114.              0              0              0
5 100    4234  2018-12-10 17:57:38 1                            369.              0              0              0
6 100    21787 2018-07-23 18:43:40 2                            244.              0              0              0
# ... with 28 more variables: sum_event1_1 <dbl>, sum_event1_2 <dbl>, sum_event1_4 <dbl>, sum_event1_5 <dbl>,
#   sum_event1_6 <dbl>, sum_event1_7 <dbl>, sum_event1_8 <dbl>, sum_event1_9 <dbl>, sum_event1_10 <dbl>,
#   sum_event1_11 <dbl>, sum_event2_1 <dbl>, sum_event2_2 <dbl>, sum_event2_3 <dbl>, sum_event2_4 <dbl>,
#   sum_event2_5 <dbl>, sum_event2_6 <dbl>, sum_event2_7 <dbl>, sum_event2_8 <dbl>, sum_event2_9 <dbl>,
#   sum_event2_10 <dbl>, avg_date_diff <dbl>, cumrev_per_prod_till_prev_order <dbl>, rev_per_prod_prev_ord <dbl>,
#   order_month <fct>, order_week_of_year <fct>, order_qtr <fct>, order_day_of_week <fct>, order_hour_of_day <fct>

The summary of the data is

summary(df)
    custno              ordno          orderdate                   prodcat1  num_days_till_last_order
 Length:179504      1974   :     5   Min.   :2016-01-01 05:05:14   1:29875   Min.   :   0.00         
 Class :character   2794   :     5   1st Qu.:2016-09-25 19:15:03   2:53510   1st Qu.:   9.65         
 Mode  :character   3657   :     5   Median :2017-06-17 17:01:47   3:36538   Median :  35.19         
                    4577   :     5   Mean   :2017-06-24 14:26:40   4:28188   Mean   : 100.02         
                    5614   :     5   3rd Qu.:2018-03-17 07:09:34   5: 9724   3rd Qu.: 127.97         
                    5949   :     5   Max.   :2019-01-02 23:54:58   7:21669   Max.   :1081.32         
                    (Other):179474                                           NA's   :99244           
 sum_category_1     sum_category_2    sum_category_3    sum_event1_1       sum_event1_2      sum_event1_4    
 Min.   : 0.00000   Min.   : 0.0000   Min.   : 0.000   Min.   : 0.00000   Min.   :0.00000   Min.   :0.00000  
 1st Qu.: 0.00000   1st Qu.: 0.0000   1st Qu.: 0.000   1st Qu.: 0.00000   1st Qu.:0.00000   1st Qu.:0.00000  
 Median : 0.00000   Median : 0.0000   Median : 0.000   Median : 0.00000   Median :0.00000   Median :0.00000  
 Mean   : 0.07668   Mean   : 0.3121   Mean   : 1.205   Mean   : 0.07388   Mean   :0.03828   Mean   :0.03738  
 3rd Qu.: 0.00000   3rd Qu.: 0.0000   3rd Qu.: 1.000   3rd Qu.: 0.00000   3rd Qu.:0.00000   3rd Qu.:0.00000  
 Max.   :25.00000   Max.   :32.0000   Max.   :55.000   Max.   :12.00000   Max.   :9.00000   Max.   :8.00000  
                                                                                                             
  sum_event1_5       sum_event1_6      sum_event1_7      sum_event1_8      sum_event1_9      sum_event1_10     
 Min.   :0.000000   Min.   :0.00000   Min.   :0.00000   Min.   :0.00000   Min.   :0.000000   Min.   :0.000000  
 1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.000000  
 Median :0.000000   Median :0.00000   Median :0.00000   Median :0.00000   Median :0.000000   Median :0.000000  
 Mean   :0.003755   Mean   :0.02283   Mean   :0.02489   Mean   :0.01826   Mean   :0.006345   Mean   :0.002201  
 3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:0.000000  
 Max.   :4.000000   Max.   :4.00000   Max.   :8.00000   Max.   :8.00000   Max.   :3.000000   Max.   :2.000000  
                                                                                                               
 sum_event1_11      sum_event2_1      sum_event2_2      sum_event2_3      sum_event2_4     sum_event2_5    
 Min.   :0.00000   Min.   : 0.0000   Min.   :0.00000   Min.   : 0.0000   Min.   : 0.000   Min.   :0.00000  
 1st Qu.:0.00000   1st Qu.: 0.0000   1st Qu.:0.00000   1st Qu.: 0.0000   1st Qu.: 0.000   1st Qu.:0.00000  
 Median :0.00000   Median : 0.0000   Median :0.00000   Median : 0.0000   Median : 0.000   Median :0.00000  
 Mean   :0.01613   Mean   : 0.1134   Mean   :0.02092   Mean   : 0.2485   Mean   : 0.202   Mean   :0.06925  
 3rd Qu.:0.00000   3rd Qu.: 0.0000   3rd Qu.:0.00000   3rd Qu.: 0.0000   3rd Qu.: 0.000   3rd Qu.:0.00000  
 Max.   :7.00000   Max.   :10.0000   Max.   :5.00000   Max.   :14.0000   Max.   :14.000   Max.   :7.00000  
                                                                                                           
  sum_event2_6      sum_event2_7      sum_event2_8      sum_event2_9     sum_event2_10      avg_date_diff    
 Min.   :0.00000   Min.   : 0.0000   Min.   : 0.0000   Min.   : 0.0000   Min.   :0.000000   Min.   :   0.00  
 1st Qu.:0.00000   1st Qu.: 0.0000   1st Qu.: 0.0000   1st Qu.: 0.0000   1st Qu.:0.000000   1st Qu.:  75.36  
 Median :0.00000   Median : 0.0000   Median : 0.0000   Median : 0.0000   Median :0.000000   Median : 204.83  
 Mean   :0.04667   Mean   : 0.5932   Mean   : 0.2288   Mean   : 0.0656   Mean   :0.006212   Mean   : 254.28  
 3rd Qu.:0.00000   3rd Qu.: 1.0000   3rd Qu.: 0.0000   3rd Qu.: 0.0000   3rd Qu.:0.000000   3rd Qu.: 390.34  
 Max.   :8.00000   Max.   :23.0000   Max.   :15.0000   Max.   :14.0000   Max.   :6.000000   Max.   :1095.07  
                                                                                            NA's   :29613    
 cumrev_per_prod_till_prev_order rev_per_prod_prev_ord  order_month    order_week_of_year order_qtr order_day_of_week
 Min.   :  0.00                  Min.   :  0.00        01     :18526   01     :  5089     1:46963   Fri:15476        
 1st Qu.:  0.00                  1st Qu.:  0.00        05     :16640   48     :  5053     2:46829   Mon:25323        
 Median :  0.00                  Median :  0.00        12     :16408   49     :  4751     3:45956   Sat:24936        
 Mean   : 33.41                  Mean   : 33.47        03     :16101   09     :  4591     4:39756   Sun:41578        
 3rd Qu.: 72.40                  3rd Qu.: 67.78        09     :15724   47     :  4414               Thu:21252        
 Max.   :149.98                  Max.   :150.00        06     :15556   36     :  4387               Tue:23498        
                                                       (Other):80549   (Other):151219               Wed:27441        
 order_hour_of_day
 19     : 14212   
 18     : 13804   
 20     : 12312   
 17     : 11324   
 12     : 10465   
 13     : 10457   
 (Other):106930   

3. Feature Selection

Lets look at the correlation between cumrev_per_prod_till_prev_order and rev_per_prod_prev_ord.

cor(df[,!names(df) %in% c("custno","ordno","orderdate","prodcat1","order_month","order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")])
                                num_days_till_last_order sum_category_1 sum_category_2 sum_category_3 sum_event1_1
num_days_till_last_order                               1             NA             NA             NA           NA
sum_category_1                                        NA     1.00000000     0.05975836     0.05260110   0.11519467
sum_category_2                                        NA     0.05975836     1.00000000     0.07901509   0.22927557
sum_category_3                                        NA     0.05260110     0.07901509     1.00000000   0.30293379
sum_event1_1                                          NA     0.11519467     0.22927557     0.30293379   1.00000000
sum_event1_2                                          NA     0.05190649     0.09216206     0.28816102   0.01454894
sum_event1_4                                          NA     0.10420820     0.09576677     0.23244340   0.01704493
sum_event1_5                                          NA     0.03355437     0.18529400     0.08942683   0.04491075
sum_event1_6                                          NA     0.05581213     0.15496074     0.19627540   0.11837647
sum_event1_7                                          NA     0.07045872     0.23373840     0.18079784   0.09322193
sum_event1_8                                          NA     0.03299169     0.12766962     0.09466138   0.03762944
sum_event1_9                                          NA     0.06742637     0.15114544     0.06032940   0.02045415
sum_event1_10                                         NA     0.02922822     0.02385869     0.09058968   0.03318439
sum_event1_11                                         NA     0.05451642     0.14847478     0.18215765   0.01259576
sum_event2_1                                          NA     0.16400344     0.39534755     0.36162396   0.32771739
sum_event2_2                                          NA     0.04884802     0.29485586     0.08132352   0.16819145
sum_event2_3                                          NA     0.14995912     0.28656827     0.69703151   0.19241359
sum_event2_4                                          NA     0.15237110     0.34116828     0.57082973   0.21609841
sum_event2_5                                          NA     0.10477098     0.28599343     0.32745477   0.13628671
sum_event2_6                                          NA     0.04255567     0.15267308     0.34292059   0.06951080
sum_event2_7                                          NA     0.21068381     0.37149552     0.79573575   0.37683835
sum_event2_8                                          NA     0.18515614     0.25965403     0.63490593   0.17223948
sum_event2_9                                          NA     0.11550660     0.19156168     0.38873940   0.15633985
sum_event2_10                                         NA     0.05779337     0.14661643     0.10350555   0.01087952
avg_date_diff                                         NA             NA             NA             NA           NA
cumrev_per_prod_till_prev_order                       NA     0.03737429     0.09659084     0.10296331   0.08923517
rev_per_prod_prev_ord                                 NA     0.03192756     0.08114139     0.09057785   0.07746783
                                sum_event1_2 sum_event1_4 sum_event1_5 sum_event1_6 sum_event1_7 sum_event1_8
num_days_till_last_order                  NA           NA           NA           NA           NA           NA
sum_category_1                   0.051906492  0.104208203  0.033554375  0.055812133  0.070458724  0.032991685
sum_category_2                   0.092162057  0.095766765  0.185293999  0.154960744  0.233738403  0.127669616
sum_category_3                   0.288161024  0.232443398  0.089426830  0.196275401  0.180797837  0.094661384
sum_event1_1                     0.014548941  0.017044927  0.044910752  0.118376472  0.093221932  0.037629442
sum_event1_2                     1.000000000  0.106593784  0.009136500  0.043475175  0.005957926  0.021141806
sum_event1_4                     0.106593784  1.000000000  0.008942886  0.045010854  0.022378707  0.016567662
sum_event1_5                     0.009136500  0.008942886  1.000000000  0.017995510  0.036413875  0.034946981
sum_event1_6                     0.043475175  0.045010854  0.017995510  1.000000000  0.039636173  0.041811518
sum_event1_7                     0.005957926  0.022378707  0.036413875  0.039636173  1.000000000  0.031112866
sum_event1_8                     0.021141806  0.016567662  0.034946981  0.041811518  0.031112866  1.000000000
sum_event1_9                     0.003642405  0.012833633  0.196932767  0.014583815  0.015925018  0.014960042
sum_event1_10                    0.009662797  0.038373035  0.023348874  0.016737109  0.049604709  0.008740903
sum_event1_11                    0.047494832  0.042077314  0.076340648  0.025817024  0.019213420  0.018179601
sum_event2_1                     0.126342528  0.078807816  0.096687948  0.138671178  0.147040927  0.067910687
sum_event2_2                     0.022814858  0.032483246  0.085843617  0.057584136  0.072103152  0.027882213
sum_event2_3                     0.193812238  0.171011851  0.089392936  0.144491018  0.143533072  0.097118603
sum_event2_4                     0.180511178  0.087272039  0.105170291  0.125912701  0.163673961  0.116403423
sum_event2_5                     0.101470000  0.083240478  0.041504383  0.083644601  0.150389508  0.037910115
sum_event2_6                     0.067632969  0.068699315  0.033706739  0.049668450  0.034505390  0.033354643
sum_event2_7                     0.327082131  0.326789177  0.158035173  0.264960597  0.270992280  0.116866673
sum_event2_8                     0.140534211  0.128928045  0.072376612  0.122953320  0.131704969  0.098336034
sum_event2_9                     0.093674460  0.053667104  0.034756614  0.087029808  0.106293839  0.054326345
sum_event2_10                    0.017897243  0.007294684  0.176119546  0.009332018  0.017093671  0.022601455
avg_date_diff                             NA           NA           NA           NA           NA           NA
cumrev_per_prod_till_prev_order  0.010570714  0.017304208  0.035784992  0.022992106  0.048528785  0.013275841
rev_per_prod_prev_ord            0.007987318  0.015210939  0.030221063  0.019222640  0.039821325  0.009511783
                                sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2 sum_event2_3
num_days_till_last_order                  NA            NA            NA           NA           NA           NA
sum_category_1                   0.067426374   0.029228220    0.05451642   0.16400344   0.04884802   0.14995912
sum_category_2                   0.151145437   0.023858692    0.14847478   0.39534755   0.29485586   0.28656827
sum_category_3                   0.060329405   0.090589681    0.18215765   0.36162396   0.08132352   0.69703151
sum_event1_1                     0.020454153   0.033184391    0.01259576   0.32771739   0.16819145   0.19241359
sum_event1_2                     0.003642405   0.009662797    0.04749483   0.12634253   0.02281486   0.19381224
sum_event1_4                     0.012833633   0.038373035    0.04207731   0.07880782   0.03248325   0.17101185
sum_event1_5                     0.196932767   0.023348874    0.07634065   0.09668795   0.08584362   0.08939294
sum_event1_6                     0.014583815   0.016737109    0.02581702   0.13867118   0.05758414   0.14449102
sum_event1_7                     0.015925018   0.049604709    0.01921342   0.14704093   0.07210315   0.14353307
sum_event1_8                     0.014960042   0.008740903    0.01817960   0.06791069   0.02788221   0.09711860
sum_event1_9                     1.000000000   0.004387925    0.02605872   0.09968675   0.14183254   0.07038604
sum_event1_10                    0.004387925   1.000000000    0.02053569   0.03751542   0.05636781   0.06519097
sum_event1_11                    0.026058724   0.020535692    1.00000000   0.07193240   0.01081409   0.11819904
sum_event2_1                     0.099686753   0.037515416    0.07193240   1.00000000   0.16491709   0.26790031
sum_event2_2                     0.141832536   0.056367806    0.01081409   0.16491709   1.00000000   0.08511606
sum_event2_3                     0.070386038   0.065190966    0.11819904   0.26790031   0.08511606   1.00000000
sum_event2_4                     0.061545179   0.043629189    0.11121592   0.24067090   0.07451285   0.38841942
sum_event2_5                     0.056381737   0.025509788    0.04451130   0.33921453   0.14850369   0.22180114
sum_event2_6                     0.046663616   0.015732748    0.06082702   0.20138925   0.10505722   0.23357347
sum_event2_7                     0.104482673   0.099699785    0.26412166   0.29528358   0.08976346   0.55632798
sum_event2_8                     0.067028737   0.051424380    0.11974492   0.23102153   0.08022814   0.43606937
sum_event2_9                     0.042963772   0.033770146    0.04548187   0.15307721   0.06487092   0.21722918
sum_event2_10                    0.071174611   0.004239591    0.45808392   0.06973166   0.01221502   0.09121469
avg_date_diff                             NA            NA            NA           NA           NA           NA
cumrev_per_prod_till_prev_order  0.031206540   0.008508288    0.01007391   0.09227581   0.04056525   0.08875024
rev_per_prod_prev_ord            0.027600647   0.007865215    0.01005484   0.07749117   0.03459262   0.07729935
                                sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9
num_days_till_last_order                  NA           NA           NA           NA           NA           NA
sum_category_1                    0.15237110   0.10477098   0.04255567   0.21068381   0.18515614   0.11550660
sum_category_2                    0.34116828   0.28599343   0.15267308   0.37149552   0.25965403   0.19156168
sum_category_3                    0.57082973   0.32745477   0.34292059   0.79573575   0.63490593   0.38873940
sum_event1_1                      0.21609841   0.13628671   0.06951080   0.37683835   0.17223948   0.15633985
sum_event1_2                      0.18051118   0.10147000   0.06763297   0.32708213   0.14053421   0.09367446
sum_event1_4                      0.08727204   0.08324048   0.06869931   0.32678918   0.12892804   0.05366710
sum_event1_5                      0.10517029   0.04150438   0.03370674   0.15803517   0.07237661   0.03475661
sum_event1_6                      0.12591270   0.08364460   0.04966845   0.26496060   0.12295332   0.08702981
sum_event1_7                      0.16367396   0.15038951   0.03450539   0.27099228   0.13170497   0.10629384
sum_event1_8                      0.11640342   0.03791011   0.03335464   0.11686667   0.09833603   0.05432635
sum_event1_9                      0.06154518   0.05638174   0.04666362   0.10448267   0.06702874   0.04296377
sum_event1_10                     0.04362919   0.02550979   0.01573275   0.09969979   0.05142438   0.03377015
sum_event1_11                     0.11121592   0.04451130   0.06082702   0.26412166   0.11974492   0.04548187
sum_event2_1                      0.24067090   0.33921453   0.20138925   0.29528358   0.23102153   0.15307721
sum_event2_2                      0.07451285   0.14850369   0.10505722   0.08976346   0.08022814   0.06487092
sum_event2_3                      0.38841942   0.22180114   0.23357347   0.55632798   0.43606937   0.21722918
sum_event2_4                      1.00000000   0.17797305   0.12239740   0.47066984   0.36524952   0.30811130
sum_event2_5                      0.17797305   1.00000000   0.27849308   0.22327941   0.19044655   0.11103355
sum_event2_6                      0.12239740   0.27849308   1.00000000   0.20742510   0.18095639   0.07453614
sum_event2_7                      0.47066984   0.22327941   0.20742510   1.00000000   0.49205418   0.30352810
sum_event2_8                      0.36524952   0.19044655   0.18095639   0.49205418   1.00000000   0.25329970
sum_event2_9                      0.30811130   0.11103355   0.07453614   0.30352810   0.25329970   1.00000000
sum_event2_10                     0.09254652   0.02866873   0.02601103   0.12694000   0.07973688   0.02847559
avg_date_diff                             NA           NA           NA           NA           NA           NA
cumrev_per_prod_till_prev_order   0.09585444   0.06096073   0.01976141   0.10435709   0.07829894   0.11248283
rev_per_prod_prev_ord             0.08400979   0.05189747   0.01556599   0.09129023   0.06764350   0.09764213
                                sum_event2_10 avg_date_diff cumrev_per_prod_till_prev_order rev_per_prod_prev_ord
num_days_till_last_order                   NA            NA                              NA                    NA
sum_category_1                    0.057793373            NA                     0.037374286           0.031927560
sum_category_2                    0.146616429            NA                     0.096590835           0.081141387
sum_category_3                    0.103505548            NA                     0.102963309           0.090577852
sum_event1_1                      0.010879520            NA                     0.089235169           0.077467828
sum_event1_2                      0.017897243            NA                     0.010570714           0.007987318
sum_event1_4                      0.007294684            NA                     0.017304208           0.015210939
sum_event1_5                      0.176119546            NA                     0.035784992           0.030221063
sum_event1_6                      0.009332018            NA                     0.022992106           0.019222640
sum_event1_7                      0.017093671            NA                     0.048528785           0.039821325
sum_event1_8                      0.022601455            NA                     0.013275841           0.009511783
sum_event1_9                      0.071174611            NA                     0.031206540           0.027600647
sum_event1_10                     0.004239591            NA                     0.008508288           0.007865215
sum_event1_11                     0.458083923            NA                     0.010073913           0.010054840
sum_event2_1                      0.069731659            NA                     0.092275805           0.077491173
sum_event2_2                      0.012215024            NA                     0.040565252           0.034592618
sum_event2_3                      0.091214686            NA                     0.088750244           0.077299347
sum_event2_4                      0.092546519            NA                     0.095854445           0.084009789
sum_event2_5                      0.028668733            NA                     0.060960725           0.051897473
sum_event2_6                      0.026011026            NA                     0.019761409           0.015565994
sum_event2_7                      0.126940002            NA                     0.104357094           0.091290228
sum_event2_8                      0.079736877            NA                     0.078298936           0.067643502
sum_event2_9                      0.028475585            NA                     0.112482827           0.097642128
sum_event2_10                     1.000000000            NA                     0.015234987           0.014600962
avg_date_diff                              NA             1                              NA                    NA
cumrev_per_prod_till_prev_order   0.015234987            NA                     1.000000000           0.880044013
rev_per_prod_prev_ord             0.014600962            NA                     0.880044013           1.000000000

This is a very high correlation.

cor(df$rev_per_prod_prev_ord,df$cumrev_per_prod_till_prev_order)
[1] 0.880044

Therefore, we will choose only one metric as a predictor, which is rev_per_prod_prev_ord.

df$cumrev_per_prod_till_prev_order <- NULL

For categorical variables, we will perform the chi-square test of association. We will compare various columns derived from orderdate.

#"custno","ordno","orderdate","prodcat1","order_month","order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day"
chisq.test(df$order_month,df$order_qtr)

    Pearson's Chi-squared test

data:  df$order_month and df$order_qtr
X-squared = 538510, df = 33, p-value < 2.2e-16
chisq.test(df$order_day_of_week,df$order_hour_of_day)

    Pearson's Chi-squared test

data:  df$order_day_of_week and df$order_hour_of_day
X-squared = 2343.5, df = 138, p-value < 2.2e-16
chisq.test(df$order_day_of_week,df$order_week_of_year)

    Pearson's Chi-squared test

data:  df$order_day_of_week and df$order_week_of_year
X-squared = 13783, df = 318, p-value < 2.2e-16

since the p-value is < 2.2e-16 is less than the cut-off value of 0.05, we can reject the null hypothesis in favor of alternative hypothesis and conclude, that the variables are dependent to each other. Therefore, we will only consider one variable for moedeling, which is order_month and delete the rest.

df[,c("order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")]<-NULL

We have removed combination of highly correlated variables and highly associated variable. During the model building phase we will encounter some variables that are not significant predictors to the response variable. In those steps, we will still be performing feature selection by removing insignificant predictors and keeping significant ones.

4. Model Designing and sampling

We have prepared the data that now we can use to fit a model. We are trying to fit a model which predicts what product category-1 is a user most likely to buy based on his past online-activity as well as his buying behaviour. We will split the data into training and test sample. We will use the training sample to fit different classification models and test sample to measure the performance of the model. The train-test split is 70-30 split, i.e., 70% of the data is used for training and 30% for testing.

## 70% of the sample size
smp_size <- floor(0.70 * nrow(df))
## set the seed to make your partition reproducible
set.seed(1234)
train_ind <- sample(seq_len(nrow(df)), size = smp_size)
train <- df[train_ind, ]
test <- df[-train_ind, ]

Our response mode is prodcat1. We need to make sure that all the classes of prodcat1 are present in train and test samples

table(train$prodcat1)

    1     2     3     4     5     7 
20958 37549 25483 19725  6735 15202 
table(test$prodcat1)

    1     2     3     4     5     7 
 8917 15961 11055  8463  2989  6467 

In the next section, we will use different modelling techniques to fit a multi-class classifcation models. We will use the following algorithms 1. Logistic regression 2. Random Forest Regression

Logistic regression works well for linear relationships and has high interpretability, whereas Random Forest can fit non-linear relationships at the cost of interpretation.

The metric we will use to determine the best model is test-AUC (Area under the curve of the ROC curve for test sample)

5. Model Generation and Evaluation

gc()
            used   (Mb) gc trigger   (Mb)   max used   (Mb)
Ncells   4653526  248.6    8120335  433.7    8120335  433.7
Vcells 133346695 1017.4 1011796314 7719.4 1264734433 9649.2

In this step we will fit different models on the training sample and predict for the test sample

Logistic Regrssion

We will fit a mutinomial logistic regression model. We will ignore num_days_till_last_order and avg_date_diff in logistic regression as they have NA values. We could impute those values but given the time constraint, we will choose to ignore them.

summary(glm)
Call:
nnet::multinom(formula = prodcat1 ~ ., data = train1)

Coefficients:
  (Intercept) sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4 sum_event1_5
2  0.92685719    -0.25976008    -0.21846016    -0.15653215  -0.08278422 -0.008287228   0.08589900    0.3483203
3 -0.01608086     0.55858920     0.59798482     0.52497554   0.20562568  0.007877831  -0.02182606    0.5742525
4  0.09354858    -0.14542476    -0.23535552    -0.01287877  -0.35066917  0.039188349   0.14924121   -0.2160810
5 -0.09783563     0.03098618     0.01213515     0.14495016  -0.03894853 -0.012121087   0.15994628    0.1169564
7 -0.47879203     0.10261985     0.12321927     0.05740280   0.22817106  0.018129963   0.02396771    0.3739307
  sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2
2   0.07178375   0.16623964    0.1702947   0.02029412    0.20154455    0.29036966  0.265228758   0.03010450
3   0.09367701   0.02787943    0.5000148   0.47598324    0.27961129   -0.06743240 -0.457797817  -0.46889749
4  -0.01427105  -0.05842807    0.3526541   0.26509099   -0.39961027    0.08591697  0.210933364  -0.33883230
5  -0.03531872   0.01817052    0.5071345   0.67521085   -0.03899443    0.06919961 -0.031773671  -0.13686801
7   0.09535578  -0.05755044    0.3329135   0.35575033    0.15869189   -0.07209661  0.004402445  -0.08104179
  sum_event2_3 sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10
2  -0.19965515   0.16281669   0.23054718   0.18446050   0.12066793   0.23223625   0.26787968   0.158417789
3  -0.59725872  -0.49968157  -0.51793239  -0.47668799  -0.57219192  -0.44079642  -0.40219788  -0.564197358
4   0.17676008  -0.07520873   0.30360473   0.68110953   0.07898073   0.13992636  -0.17966297   0.002290715
5  -0.05680272  -0.15363637  -0.01972262   0.14761678  -0.14574022   0.03230797  -0.07199110  -0.597848602
7  -0.13424732  -0.05260009  -0.04518582  -0.05837584  -0.10786851   0.04617076   0.09463892  -0.265430886
  rev_per_prod_prev_ord order_month02 order_month03 order_month04 order_month05 order_month06 order_month07
2          0.0053273175    0.06670542   -0.45679105    -0.6132285   -0.37591534    -0.1397130    0.15680028
3          0.0071552592    0.28015000   -0.02144347    -0.4644083   -0.02060058     0.3571499    0.53346173
4          0.0032106312   -0.15238535   -0.06834588    -0.7880644   -0.52247659     0.3878547    0.08487551
5          0.0009114869   -1.19706345   -2.29136974    -3.0809798   -2.83136757    -2.2205060   -1.96490684
7          0.0048534076    0.12131887   -0.15204343    -0.4647843   -0.06303049     0.2404515    0.31380264
  order_month08 order_month09 order_month10 order_month11 order_month12
2    0.08873367   -0.05275182   -0.86105906    -1.6318948   -1.22583565
3    0.52023102    0.27756253   -0.39333021    -1.1316142   -0.63581421
4   -0.02500962    0.27402639   -0.92151454    -1.6003521   -1.05343164
5   -1.50390169   -2.04718750   -0.92900361    -0.9209117   -0.11145054
7    0.35897002    0.11152224   -0.06629529    -0.4029704   -0.03868497

Std. Errors:
  (Intercept) sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4 sum_event1_5
2  0.02945365     0.17988685     0.17922265     0.17902124   0.03476902   0.04343567   0.04584102    0.1786825
3  0.03393588     0.03838143     0.03580656     0.03552862   0.03130057   0.04323451   0.04819045    0.1654328
4  0.03353468     0.09035515     0.08901041     0.08852505   0.04016560   0.04235464   0.04569478    0.2270410
5  0.03582922     0.03272326     0.02350971     0.02113128   0.04332606   0.05688463   0.05848935    0.2592145
7  0.03878963     0.04114675     0.03837509     0.03808549   0.03365701   0.04832331   0.05311936    0.1847943
  sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2
2   0.06164166   0.05155020   0.07101928    0.1366665     0.1949923    0.06984685   0.18072836   0.18900791
3   0.06104808   0.05080723   0.06691153    0.1229846     0.1916470    0.07820674   0.04422801   0.06451373
4   0.06646928   0.05944062   0.07303186    0.1446586     0.2266176    0.07769831   0.09302578   0.11676610
5   0.09005482   0.07406142   0.08587598    0.1685918     0.3068402    0.11487523   0.04243847   0.09207128
7   0.06780314   0.05758238   0.07535617    0.1364164     0.2244613    0.09060666   0.04783762   0.07171956
  sum_event2_3 sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10
2   0.18014630   0.18014371   0.18180052   0.18463314   0.17925412   0.17959376   0.18214907     0.2094330
3   0.03974465   0.04044870   0.04928406   0.05686271   0.03731785   0.04041361   0.04874715     0.1178595
4   0.09038571   0.09104484   0.09507335   0.09726251   0.08934447   0.09055962   0.09726662     0.1503641
5   0.03185839   0.03446989   0.05159846   0.05848379   0.02674471   0.03299538   0.05096873     0.1970621
7   0.04298014   0.04384333   0.05366494   0.06322264   0.04013347   0.04360766   0.05263676     0.1395643
  rev_per_prod_prev_ord order_month02 order_month03 order_month04 order_month05 order_month06 order_month07
2          0.0002169191    0.04530423    0.04083369    0.03930674    0.03960859    0.04359164    0.04377803
3          0.0002276530    0.05078367    0.04551531    0.04568981    0.04462479    0.04782732    0.04815532
4          0.0002525343    0.05303935    0.04543052    0.04728159    0.04688303    0.04730412    0.04997951
5          0.0003425137    0.07165402    0.08381117    0.10439219    0.09946907    0.09460615    0.08901990
7          0.0002559565    0.05893696    0.05309151    0.05305669    0.05139468    0.05493363    0.05560687
  order_month08 order_month09 order_month10 order_month11 order_month12
2    0.04450789    0.04296455    0.05119891    0.04178776    0.04281439
3    0.04870952    0.04775199    0.05518960    0.04628534    0.04657055
4    0.05126673    0.04738420    0.06209392    0.05085691    0.04976748
5    0.07707928    0.08703584    0.06894489    0.04962812    0.04784662
7    0.05584312    0.05537830    0.06084246    0.04930314    0.05038297

Residual Deviance: 402777.3 
AIC: 403137.3 

Now we’ll calculate Z score and p-Value for the variables in the model.

z <- summary(glm)$coefficients/summary(glm)$standard.errors

Calculating the the odds ratio coefficient for each predictor

exp(coef(glm))
  (Intercept) sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4 sum_event1_5
2   2.5265562      0.7712366      0.8037555      0.8551040    0.9205498    0.9917470    1.0896963    1.4166860
3   0.9840478      1.7482044      1.8184506      1.6904175    1.2282933    1.0079089    0.9784104    1.7758026
4   1.0980639      0.8646549      0.7902898      0.9872038    0.7042167    1.0399663    1.1609530    0.8056701
5   0.9067979      1.0314713      1.0122091      1.1559820    0.9618002    0.9879521    1.1734478    1.1240704
7   0.6195313      1.1080701      1.1311324      1.0590823    1.2563002    1.0182953    1.0242572    1.4534364
  sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2
2    1.0744230    1.1808560     1.185654     1.020501     1.2232907     1.3369216    1.3037292    1.0305622
3    1.0982050    1.0282717     1.648746     1.609596     1.3226156     0.9347909    0.6326754    0.6256917
4    0.9858303    0.9432461     1.422839     1.303550     0.6705813     1.0897158    1.2348301    0.7126019
5    0.9652977    1.0183366     1.660526     1.964447     0.9617561     1.0716501    0.9687258    0.8720853
7    1.1000502    0.9440743     1.395027     1.427251     1.1719768     0.9304410    1.0044122    0.9221552
  sum_event2_3 sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10
2    0.8190131    1.1768210    1.2592889    1.2025695    1.1282502    1.2614177    1.3071898     1.1716556
3    0.5503181    0.6067238    0.5957511    0.6208362    0.5642872    0.6435237    0.6688484     0.5688165
4    1.1933447    0.9275499    1.3547335    1.9760690    1.0821835    1.1501891    0.8355518     1.0022933
5    0.9447804    0.8575838    0.9804706    1.1590686    0.8643822    1.0328355    0.9305392     0.5499936
7    0.8743738    0.9487594    0.9558199    0.9432954    0.8977456    1.0472532    1.0992619     0.7668754
  rev_per_prod_prev_ord order_month02 order_month03 order_month04 order_month05 order_month06 order_month07
2              1.005342     1.0689805     0.6333127    0.54159947     0.6866605     0.8696078     1.1697620
3              1.007181     1.3233283     0.9787848    0.62850687     0.9796102     1.4292500     1.7048237
4              1.003216     0.8586573     0.9339374    0.45472411     0.5930500     1.4738156     1.0885815
5              1.000912     0.3020800     0.1011278    0.04591425     0.0589322     0.1085542     0.1401689
7              1.004865     1.1289849     0.8589510    0.62827063     0.9389148     1.2718232     1.3686196
  order_month08 order_month09 order_month10 order_month11 order_month12
2     1.0927896     0.9486154     0.4227142     0.1955587     0.2935123
3     1.6824163     1.3199086     0.6748059     0.3225122     0.5295042
4     0.9753005     1.3152495     0.3979159     0.2018254     0.3487389
5     0.2222613     0.1290975     0.3949470     0.3981559     0.8945356
7     1.4318539     1.1179786     0.9358545     0.6683319     0.9620537

Calculate Variable importance (absolute value of t-statistic)

varimp_glm %>% arrange(desc(importance))
   importance             predictor
1  5.68774320         order_month11
2  5.41146528         order_month04
3  3.81339058         order_month05
4  3.34567502         order_month06
5  3.17120271         order_month10
6  3.06521701         order_month12
7  3.05384700         order_month07
8  2.98999357         order_month03
9  2.76305048         order_month09
10 2.49684603         order_month08
11 1.86301165          sum_event1_8
12 1.81762310         order_month02
13 1.79232953          sum_event1_9
14 1.62954085          sum_event1_5
15 1.58818535         sum_event2_10
16 1.54825064          sum_event2_6
17 1.18715492        sum_category_2
18 1.16472398          sum_event2_3
19 1.11699275          sum_event2_5
20 1.09738007        sum_category_1
21 1.07845244         sum_event1_10
22 1.05574408          sum_event2_2
23 1.02544930          sum_event2_7
24 1.01637055          sum_event2_9
25 0.97013605          sum_event2_1
26 0.94394345          sum_event2_4
27 0.90619866          sum_event1_1
28 0.89673941        sum_category_3
29 0.89143776          sum_event2_8
30 0.58501525         sum_event1_11
31 0.44088025          sum_event1_4
32 0.32826810          sum_event1_7
33 0.31040629          sum_event1_6
34 0.08560446          sum_event1_2
35 0.02145810 rev_per_prod_prev_ord

We can see that order month is the most important parameter. This is evident from the time series trends that we observed while exploring the data. Other important variables were sum_event1_8 ,sum_event1_8, and sum_event1_5

Let’s check for fitted values now.

head(fitted(glm))
          1         2         3          4          5          7
1 0.1362019 0.3347793 0.1507843 0.14873830 0.13157759 0.09791863
2 0.2078132 0.2037986 0.1576077 0.09417795 0.17682666 0.15977590
3 0.1982757 0.2971629 0.1782158 0.21250755 0.01799667 0.09584135
4 0.1406811 0.3090922 0.1978609 0.22767029 0.01384818 0.11084742
5 0.1918412 0.3069652 0.1847759 0.19673760 0.01759233 0.10208775
6 0.1406811 0.3090922 0.1978609 0.22767029 0.01384818 0.11084742

predicting on the test data

predict_tst=as.data.frame(predict(glm,test1,type="probs"))
colnames(predict_tst)<-sapply(colnames(predict_tst), function(x) paste('logit_',x,sep = ""))
predict_tst$predicted_class<-apply(predict_tst,1,which.max)
predict_tst$predicted_class<-ifelse(predict_tst$predicted_class==6,7,predict_tst$predicted_class)
head(predict_tst)
    logit_1   logit_2   logit_3    logit_4    logit_5   logit_7 predicted_class
1 0.1406811 0.3090922 0.1978609 0.22767029 0.01384818 0.1108474               2
2 0.3020623 0.1545535 0.1508060 0.09982670 0.12735199 0.1653995               1
3 0.1137407 0.2836578 0.3157333 0.12195955 0.01317366 0.1517349               3
4 0.1918412 0.3069652 0.1847759 0.19673760 0.01759233 0.1020877               2
5 0.1550755 0.2313376 0.2066006 0.09049224 0.14177102 0.1747231               2
6 0.1305176 0.3721515 0.2088617 0.16667300 0.01657632 0.1052199               2

Creating confusion matrix for test sample

tab<-table(predict_tst$predicted_class,test1$prodcat1)
library(caret) 
conf<-confusionMatrix(tab)
conf
Confusion Matrix and Statistics

   
        1     2     3     4     5     7
  1  1744  1091  1018   617   919  1090
  2  6219 13703  8312  6233  1550  4407
  3   489   607  1155   326   176   590
  4   336   446   419  1167   146   246
  5   108    91   118   114   183   113
  7    21    23    33     6    15    21

Overall Statistics
                                          
               Accuracy : 0.3337          
                 95% CI : (0.3298, 0.3377)
    No Information Rate : 0.2964          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.0945          
 Mcnemar's Test P-Value : < 2.2e-16       

Statistics by Class:

                     Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 7
Sensitivity           0.19558   0.8585  0.10448  0.13789 0.061224 0.003247
Specificity           0.89463   0.2948  0.94887  0.96490 0.989305 0.997932
Pos Pred Value        0.26918   0.3390  0.34550  0.42283 0.251719 0.176471
Neg Pred Value        0.84858   0.8318  0.80400  0.85720 0.947181 0.880036
Prevalence            0.16558   0.2964  0.20528  0.15715 0.055504 0.120088
Detection Rate        0.03239   0.2545  0.02145  0.02167 0.003398 0.000390
Detection Prevalence  0.12031   0.7506  0.06208  0.05125 0.013500 0.002210
Balanced Accuracy     0.54510   0.5767  0.52668  0.55140 0.525265 0.500590

Class2 has high sensitivity, which means the model has a higher True Positive Rate for Class2. This means that the model does a good job of predicting whether a customer will will buy product category 2. At the same time it does a poor job of predicting whether a customer is not going to buy a product from prodcat2 or not. This is evident from the specificity of Class2

If we we look at the sensitivity and specificity across all the other classes, we will see that the sensitivity values are low and specificity values are high. This means that, for the other classes the model does a better job identifying whether a customer is not going to buy a product in that class than predicting whether a customer is going to buy a product in that class

Calculating Test AUC of the ROC curve. The AUC is a measure of how well a model does a job of distinguishing between classes

library(HandTill2001)
auc(multcap(response=test1$prodcat1,predicted = predict(glm,test1,type="probs")))
[1] 0.652249

This is a decent value. But it could be improved further by using complex models.

Random Forest Classification

# train1<- train
# test1<- test
# train1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
# test1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
library(randomForest)
# Fit the model
set.seed(1234)
rf <- randomForest(prodcat1 ~., data = train1, ntree=500, mtry=round(sqrt(ncol(train)-1)), importance=TRUE)
# Summarize the model
rf

Call:
 randomForest(formula = prodcat1 ~ ., data = train1, ntree = 500,      mtry = round(sqrt(ncol(train) - 1)), importance = TRUE) 
               Type of random forest: classification
                     Number of trees: 500
No. of variables tried at each split: 5

        OOB estimate of  error rate: 66.58%
Confusion matrix:
     1     2    3    4   5   7 class.error
1 4842 12678 1414 1321 359 344   0.7689665
2 3180 29391 2379 1889 279 431   0.2172628
3 2710 16849 3334 1560 289 741   0.8691677
4 1882 12550 1175 3672 278 168   0.8138403
5 2048  3063  419  563 472 170   0.9299183
7 2540  9327 1965  815 267 288   0.9810551

Calculate Variable importance

varImp(rf)
                                1         2          3          4           5           7
sum_category_1         -5.1193393 43.557678 -24.368299  -9.375528  -2.3120335 -14.4477247
sum_category_2          5.3160834 67.981092 -18.337293 -11.836191  -0.1298790 -17.6503732
sum_category_3         -0.2800313 56.653897 -39.581179  27.917861  15.0713591 -38.6677828
sum_event1_1           17.1193495 31.637741 -12.529545  -5.440176  -3.7171077  -6.3085222
sum_event1_2            0.7737313 12.986533  -9.571350  -8.408507   0.3338238  -2.8592123
sum_event1_4           -2.0829410 14.300008  -6.252205 -11.700814   6.9362477  -9.8811662
sum_event1_5            4.8315502  9.508437   4.800939   8.999123  10.6495981  -0.5754956
sum_event1_6            6.0840557 17.179022 -14.475398  -7.191722  13.7507759  -8.3775457
sum_event1_7            0.6309928 12.988774  -4.969941 -15.301061   3.5977528  -6.7350553
sum_event1_8            1.6809914 26.299258 -11.317356 -10.896376  15.3511229  -2.5753725
sum_event1_9            3.8090363 15.657352  -1.720984  -2.980269   1.7098612  -8.2161648
sum_event1_10           4.3594627  3.671061   4.854107  -7.998542   0.9822861  -2.0048350
sum_event1_11           5.2903459 13.209633  -2.836639 -11.024353   2.3213302  -4.2730299
sum_event2_1            7.3919165 27.925765 -18.059779 -14.395289  -3.2902597 -18.8961765
sum_event2_2            0.1331095 25.161970 -11.042390  -1.391763   0.3898599 -12.1770148
sum_event2_3          -18.2321937 75.808697 -28.973634  23.285029  15.4449986 -23.8456466
sum_event2_4            2.6477241 28.206531 -14.937120 -35.242783  -6.7149926 -14.6255530
sum_event2_5            4.4391053 27.434754 -18.862426  -4.914085  -3.5118249 -14.1544791
sum_event2_6            3.0745857 41.172743 -17.347414  28.037381   8.6371019 -13.9914822
sum_event2_7           -4.1280749 34.081676 -23.000965  -9.888816  -0.3076361 -25.7277140
sum_event2_8            5.5807164 26.837586 -19.050343 -10.967575   1.9857983 -17.0012923
sum_event2_9            2.5006326 24.550648 -15.510322  -9.932935   4.9804470  -9.4825662
sum_event2_10           6.4064705  8.803003  -5.048304  -7.585508   3.5674212  -3.2029759
rev_per_prod_prev_ord  -8.2350514 29.043473  29.737574  38.254197  -2.4392634   2.9193443
order_month            39.6092151 67.915286  17.223029  60.407128 106.0496162   8.1327850

Similar to what we have observed in the multinomial logistic regression, we can see that order month is the most important predictor.

predicting on the test data

head(predict_tst_rf)
   rf_1  rf_2  rf_3  rf_4  rf_5  rf_7 predicted_class_rf
1 0.000 1.000 0.000 0.000 0.000 0.000                  2
2 0.862 0.056 0.020 0.046 0.008 0.008                  1
3 0.050 0.298 0.294 0.192 0.016 0.150                  2
4 0.002 0.998 0.000 0.000 0.000 0.000                  2
5 0.204 0.552 0.064 0.000 0.124 0.056                  2
6 0.002 0.998 0.000 0.000 0.000 0.000                  2

Creating confusion matrix for test sample

tab_rf<-table(predict_tst_rf$predicted_class_rf,test1$prodcat1)
library(caret) 
conf_rf<-confusionMatrix(tab_rf)
conf_rf
Confusion Matrix and Statistics

   
        1     2     3     4     5     7
  1  2014  1402  1189   787   945  1108
  2  5430 12475  7323  5457  1323  3934
  3   613  1024  1453   501   164   843
  4   601   780   644  1538   278   331
  5   111   112   132   104   195   117
  7   148   168   314    76    84   134

Overall Statistics
                                          
               Accuracy : 0.3307          
                 95% CI : (0.3267, 0.3347)
    No Information Rate : 0.2964          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.1037          
 Mcnemar's Test P-Value : < 2.2e-16       

Statistics by Class:

                     Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 7
Sensitivity            0.2259   0.7816  0.13143  0.18173 0.065239 0.020721
Specificity            0.8791   0.3807  0.92651  0.94197 0.988675 0.983328
Pos Pred Value         0.2705   0.3471  0.31601  0.36865 0.252918 0.145022
Neg Pred Value         0.8513   0.8054  0.80505  0.86061 0.947363 0.880347
Prevalence             0.1656   0.2964  0.20528  0.15715 0.055504 0.120088
Detection Rate         0.0374   0.2317  0.02698  0.02856 0.003621 0.002488
Detection Prevalence   0.1382   0.6674  0.08538  0.07747 0.014317 0.017158
Balanced Accuracy      0.5525   0.5811  0.52897  0.56185 0.526957 0.502024

The accuracy of the model is similar to the multinomial logisitic regression. Even the sensitivity and specificity across the classes is similar to multinomial logistic regression. Class 2 has high sensitivity and low specificity and all the other classes have low sensitivity and high specificity.

Calculating Test AUC of the ROC curve

library(HandTill2001)
auc(multcap(response=test$prodcat1,predicted = predict(rf,test1,type="prob")))
[1] 0.5773988

The random forest model has better fit on the training data, as evident from the model summary, but it does not do a job better than multinomial logistic regression to seperate the classes. One possible reason could be that we did not choose that big of an ensemble. The number of trees that we choose in the forest were only 500. If we increase it, the performance will improve.

Random Forest with hyper parameter tuning

We tune the hyperparameters of random forest model so that it can converge on a more optimal output. There are two hyper parameters of the random forest

1. mtry: number of predictors randomly chosen for the decision trees in the forests 2. ntree: total number of decision trees in the forest.

One caveat though, this process requires a lot of computation and takes some time to converge.

levels(train1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
levels(test1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
library(tidyverse)
library(caret)
library(randomForest)
customRF <- list(type = "Classification", library = "randomForest", loop = NULL)
customRF$parameters <- data.frame(parameter = c("mtry", "ntree"), class = rep("numeric", 2), label = c("mtry", "ntree"))
customRF$grid <- function(x, y, len = NULL, search = "grid") {}
customRF$fit <- function(x, y, wts, param, lev, last, weights, classProbs, ...) {
  randomForest(x, y, mtry = param$mtry, ntree=param$ntree, ...)
}
customRF$predict <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
  predict(modelFit, newdata)
customRF$prob <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
  predict(modelFit, newdata, type = "prob")
customRF$sort <- function(x) x[order(x[,1]),]
customRF$levels <- function(x) x$classes
control <- trainControl(method="cv", number=10, #repeats=3, 
                        classProbs = TRUE)
tunegrid <- expand.grid(.mtry=c(15:18), .ntree=c(500, 1000))
set.seed(1234)
custom <- train(prodcat1~., data=train1, method=customRF, metric="ROC", tuneGrid=tunegrid, trControl=control)
summary(custom)
plot(custom)

I have included the code but has not run it as it takes a lot of time to run and knit the report.

6. Summary

To summarise, we had the customer order data as well as customer online activity data. We explored the data and found out that there is a seasonality in the revenue, number of orders, as well as the online activity. It peaks during Nov and Dec and drops during the months of Feb and Oct. We also saw that this trend is consitent across browsing categories as well as differnet online events. We also found out that most of the online activity is done on browsing category 3.

We also tried associating customer order data with online behaviour. While doing so, we made an assumption
*1. Only the last 30 days of online activity drives buying behaviour for a customer.
Any activity before that does not affect buying behaviour significantly. Based on this assumption, we have merged the online data with the order data. We were also able to derive som metrics like, count of each online event before the purchase, Number of days since last order, order month etc. We have used this metric to predict product category-1.

The predictive problem we are trying to solve is: Based on historical purchases and online beviour, what is the likelihood that a customer would purchase a product from a product-category1. To fit and measure the performance of the model, we first split the data into training and test sample. 70% of the data is used for training and 30% for measure its performance on unseen data. We have tried multinomial logistic regression, random forest, and random forest with hyper parameter tuning. Both the models performed decent on the test data. The models are good at identifying whether a customer is not going to buy from a particular product-category. The AUC value shows that the model does a decent job of separating classes in logistic regression. To improve the performance of the random forest model, we can perform hyperparameter tuning using a grid-search approach. This process takes a lot of time and computation capacity. I have shared the code for doing that.

With a better predicitve power, we can predict with high accuracy the product category where a customer is mostly likely to shop from. We can use this information to run targeted campaign or provide incentive to buy back from us.

---
title: "R Notebook"
output: html_notebook
---

#Data Science Homework - Homework assignment for Data Scientist candidate

#####Loading the needed libraries and setting the working directory

```{r}

library(tidyverse)
library(lubridate)
rm(list=ls())
getwd()
setwd('C:/Users/KPatel/OneDrive - CBRE, Inc/Documents/career/Shutterfly')
```

#####Importing the data from the zip file
```{r}
order <- read.table(unz("data.zip", "order.csv"), header=T, quote="\"", sep=",")
online<- read.table(unz("data.zip", "online.csv"), header=T, quote="\"", sep=",")
```


##1. Exploration and understanding of the data sets

###Order dataset
Lets look at the structure of the data
```{r}
str(order)
```
we can see that the custno, ordno, prodcat2, prodcat1 are integer but should be factors. Also, orderdate is a factor which should be a Datetime column. Changing the data type of these columns.
```{r}
order[c('custno','ordno','prodcat1','prodcat2')] <- lapply(order[c('custno','ordno','prodcat1','prodcat2')], factor)  ## as.factor() could also be used

order$orderdate <- strptime(x = as.character(order$orderdate),
                                format = "%Y-%m-%d %H:%M:%S")
order$orderdate <- as.POSIXct(order$orderdate, tz = "", format="%Y-%m-%d %H:%M:%S")

str(order)
```

Now lets look at the summary of the data.
```{r}
summary(order)
```
We can see that we have the order data for years 2016, 2017, and 2018. We can also see that there are some missing values in prodcat2.

Lets explore at prodcat2
```{r}
length(unique(order$prodcat2))
```
We have 252 levels in the prodcat2 categorical variable. Lets try to understand the mapping between prodcat1 and prodcat2
```{r}
tab<-table(order$prodcat2,order$prodcat1)
head(tab,50)
```
There are also NA's in the prodcat2.
```{r}
summary(order$prodcat2)
```
There are 1823 NA's in the prodcat2 field. We could impute these values using statistical methods. However, given the time-constraint, we won't dive deep into prodcat2.

Lets first understand the level of the data. Intuitively, it looks like that the data is at product level. Lets check that by aggregating data.
```{r}
level_ord<- order %>% group_by(custno,ordno,orderdate,prodcat1,prodcat2) %>% summarise(cnt=n()) %>% arrange(desc(cnt))
head(level_ord)
```

We can see that for custno 9 and ordno 23204, we are getting the cnt of more than 1 for each combination of prodcat1 and prodcat2. Lets look at the order data for this case
```{r}
order %>% filter(custno==9,ordno==23204)
```
We clearly see from the above example that the data is at product level. Lets get it at order and prodcat1 level.
```{r}
order_agg<- order %>% group_by(custno,ordno,orderdate,prodcat1) %>% summarise(revenue = sum(revenue), num_prod = n())
head(order_agg,10)
```



Lets look at revenue.
```{r}
summary(order$revenue)

hist(order$revenue,breaks = 30)
```
We can see from the histogram that revenue is uniformly distributed. Lets check revenue and ordersize across different prodcat1 and customers
```{r}
order %>% group_by(prodcat1) %>% summarise(avg_rev_per_product=mean(revenue),total_rev=sum(revenue),num_orders=length(unique(ordno)),cnt_cust=length(unique(custno)))
```
From the above data we can see that the prodcat1=1 has the highest sales volume both in terms of revenue, number of orders as well as number of customers, whereas prodcat1=5 has the lowest.


Lets look at trend in revenue with time
```{r fig.width=9}
library(lubridate)


order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue)) + geom_bar(stat='identity')+
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")

```
We can see a seasonlaity here. The Revenue peaks during the months of Dec and Jan. It then drops during the month of Feb and starts rising again and reaches another peak around May-June and then plunges in Oct. Then it rises again and peaks in Dec-Jan. The highest revenue was earned in Jan-2017 and lowest in Oct-2018.Lets break it down across product category and see if we get any seasonality across prodcat1. 

```{r fig.width=15, fig.height=10}
order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month,prodcat1) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue,color=prodcat1,group=prodcat1)) +                    geom_line()+ facet_wrap(~prodcat1,nrow=3, scales = 'free') +
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")


```
We can see a seasonality across all the prodcat1 similar to the overall revenue category

We expect a similar trend for num_products ordered. Lets calculate the correlation between revenue and number of products ordered.

```{r}
cor(order_agg$revenue,order_agg$num_prod)
```
The two fields are highly correlated which is evident from the scatter-plot given below
```{r}
order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()
```

Lets look at the scatterplot across each product category and calculate the correlation at that level.
```{r fig.width=15, fig.height=10}
order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()+ facet_wrap(~prodcat1,nrow=3, scales = 'free')
```

```{r}
order_agg %>% group_by(prodcat1) %>% summarise(cor_rev_prod=cor(revenue,num_prod))
```
The correlation across each prodcat1 is high.


###Online dataset
Lets look at the structure of the data
```{r}
str(online)
```

The categorical columns custno, category, event1, event2, session, and visitor are in integer and the dt column should be of datetime datetype.
```{r}
online[c('session','visitor','custno','category','event1','event2')] <- lapply(online[c('session','visitor','custno','category','event1','event2')], factor)  ## as.factor() could also be used

online$dt <- strptime(x = as.character(online$dt),
                                format = "%Y-%m-%d %H:%M:%S")
online$dt <- as.POSIXct(online$dt, tz = "", format="%Y-%m-%d %H:%M:%S")

str(online)
```

Lets look at the summary of the data
```{r}
summary(online)
```
We can see that the duration of the online data is from Jan-2016 to Dec-2017. We have 3 levels in online browsing category and multiple levels in event1 and event2. Lets first compare the number of customers in online vs order.
```{r}
length(unique(online$custno))
length(unique(order$custno))
```
There are 57584 customers in online and 70264 customers in the order dataset. Getting a list of customers common to both the datasets
```{r}
common_cust<-unique(order[which(order$custno %in% unique(online$custno)),]$custno)
length(common_cust)
```
Lets calculate online activity across each of online browsing categories.
```{r}
online %>% group_by(category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))
```
Here activity means any sort of activity, be it creation of session, change in event1 or event2 etc. Unique sessions is the count of unique sessions created on each category and new_cust is the number of unique customers that used that category. Here, online browsing category could mean which device or what channel is used by the customer to browse the website.

Moving onto event1, we can see that majority of the values in that field are null
```{r}
prop.table(table(online$event1,useNA = "ifany"))*100
```
83% of the values are null in event1. We will assume here that all the null values in event1 belong to one class which is class 0.
```{r}
levels(online$event1)
online$event1<-factor(ifelse(is.na(online$event1), 0, paste(online$event1)), levels = c(levels(online$event1), 0))
levels(online$event1)
prop.table(table(online$event1))*100
```


Lets look at event2,
```{r}
prop.table(table(online$event2,useNA = "ifany"))*100
```
We can see that event2 is a highly imbalanced class with 39% of the data is in class 7 and 14% in class3. Lets look at online activity across each of the class in event2.
```{r}
online %>% group_by(event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))
```
AS expected, most of the activity is across class7 followed by class3 and class8. However, its still not enough to tell us what the value of each those class means.

Lets look at the time series trends of online activity
```{r fig.width=11, fig.height=4}
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+ theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

We will further break it down by browsing category
```{r fig.width=11, fig.height=6}
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~category, nrow=2,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```


Lets break down online activity by event2.
```{r fig.height=15}
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~event2, nrow=5,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```


From all the online activity plot, we can see a seasonality trend. The online activity starts peaking from Nov till Jan then falls to the lowest in Feb. It then remains pretty steady till Oct. This trend is similar to the one we obtained for revenue and number of orders.

##2.Feature engineering
Lets try to understand the level of the data in online dataset.
```{r}
level_online<-online %>% group_by(session,custno,dt,event1,event2)%>% summarise(cnt=n()) %>% arrange(desc(cnt)) 
head(level_online)
```
We can see that each record is uniquely identified at session, customer, datetime, event1, and event2. Lets change the level of the data by spreading the online data on event2
```{r}
online$val<-1
online_spread_e2<-spread(online,event2,val,fill=0,sep = '_')
head(online_spread_e2)
online$val<-NULL
```
We will further spread the online data on key event1.
```{r}
online_spread_e2$val<-1
online_spread_e2e1<-spread(online_spread_e2,event1,val,fill=0,sep = '_')

head(online_spread_e2e1)
```

There is also a possibility that a customer can use different browsing categories (for example, custno 6). To account for that we have to spread the data by category as well.
```{r}
online_spread_e2e1$val<-1
online_spread_e2e1cat<-spread(online_spread_e2e1,category,val,fill=0,sep = '_')

head(online_spread_e2e1cat)
```

Now, we will engineer features from Order data. One set of important features are is the revenue made by a customer on the last order of the same product category as well as and the number number of items ordered the last time. I have created those features below

```{r}

order_agg<- order_agg %>% arrange(custno,prodcat1,orderdate,) %>% group_by(custno, prodcat1) %>% mutate(cum_rev=cumsum(revenue), cum_num_prod=cumsum(num_prod))


order_agg$cumrev_till_prev_order <- order_agg$cum_rev - order_agg$revenue
order_agg$cumnum_prod_till_prev_order <- order_agg$cum_num_prod - order_agg$num_prod
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
  group_by(custno,prodcat1) %>%
  mutate(rev_prev_ord = dplyr::lag(revenue, n = 1, default = 0),num_prod_prev_ord = dplyr::lag(num_prod, n = 1, default = 0))

order_agg[,c("revenue","num_prod","cum_rev","cum_num_prod")]<-NULL
summary(order_agg)
```
The following four metrics are created.
*1. cum_rev_till_prev_order: This is the cumulative revenue of a customer till previous order
*2. cumnum_prod_till_prev_order: Cumulative number of items till previous order.
*3. rev_prev_order: revenue made from previous order
*4. num_prod_prev_order: Number of items ordered from previous order

Another important metric would be number of days till last order
```{r}
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
  group_by(custno,prodcat1) %>%
  mutate(orderdate_prev_ord = dplyr::lag(orderdate, n = 1, default = NA))

order_agg$num_days_till_last_order <- difftime(order_agg$orderdate, order_agg$orderdate_prev_ord, units="days")

order_agg$orderdate_prev_ord<-NULL

order_agg$num_days_till_last_order <-as.numeric(order_agg$num_days_till_last_order)

summary(order_agg$num_days_till_last_order)
```

The order aggregate data now looks like.
```{r}
head(order_agg,10)
```


Now lets join the above data with order_agg data (order data aggregated at order-prodcat1 level). We will join order_agg with prodcat1 on the inequality. Since we are planning to predict prodcat1, we will put order_agg on the left and perform a left join.
```{r}
joined_df<-left_join(order_agg,online_spread_e2e1cat,by="custno") 
joined_df[,13:36][is.na(joined_df[,13:36])] <- 0



joined_df$dt<- as.character(joined_df$dt)

joined_df$dt<-ifelse(joined_df$dt>joined_df$orderdate,NA,joined_df$dt)


joined_df$dt <- strptime(x = as.character(joined_df$dt),
                                format = "%Y-%m-%d %H:%M:%S")
joined_df$dt <- as.POSIXct(joined_df$dt, tz = "", format="%Y-%m-%d %H:%M:%S")

joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")]<-lapply(joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")], function(x) ifelse(is.na(joined_df$dt)==TRUE,NA,x))

joined_df<- joined_df %>% filter(orderdate>=dt | is.na(dt)==TRUE)
head(joined_df,20)
```
as you can see for a customer with a given orderno and prodcat1, only the online activity on or before the time of the order is joined. Now lets calculate the difference between orderdate and dt.
Note: We are also incluing the order data for which no online data is available

```{r}
joined_df$date_diff<- difftime(joined_df$orderdate,joined_df$dt,units = 'days')
head(joined_df,20)
```

We are assuming that only the last 30 days of online activity drives buying behaviour. Therefor we will only consider online activities and browsing category that occured 30 days before a transaction.

```{r}
joined_df1 <- joined_df %>% filter(date_diff<=30 | is.na(date_diff)==TRUE)
joined_df2 <- joined_df %>% filter(date_diff>30)
joined_df2[,13:36]=0
joined_df_new <- rbind(joined_df1,joined_df2)
joined_df_new[, 13:36][is.na(joined_df_new[, 13:36])] <- 0

head(joined_df_new,20)
```
What we have done above is for date difference greater than 30 days, we have changed the events flags (event2_1, event2_2 etc.) and to browsing category flags to 0 as we are not considering those events to have an impact on the buying behaviour. Now we will aggregate the data by taking the count of each events and categories. This count will be the number of times that event has happened (or browsing category used) in the past 30 days before a transaction.

Now we will aggregate the data to order-prodcat1 level

```{r}
df<- joined_df_new %>% group_by(custno,ordno,orderdate,prodcat1,cumrev_till_prev_order,cumnum_prod_till_prev_order,rev_prev_ord,num_prod_prev_ord,num_days_till_last_order) %>% 
  summarise(sum_category_1 = sum(category_1),
            sum_category_2 = sum(category_2),
            sum_category_3 = sum(category_3),
            sum_event1_1 = sum(event1_1),
            sum_event1_2 = sum(event1_2),
            sum_event1_4 = sum(event1_4),
            sum_event1_5 = sum(event1_5),
            sum_event1_6 = sum(event1_6),
            sum_event1_7 = sum(event1_7),
            sum_event1_8 = sum(event1_8),
            sum_event1_9 = sum(event1_9),
            sum_event1_10 = sum(event1_10),
            sum_event1_11 = sum(event1_11),
            sum_event2_1 = sum(event2_1),
            sum_event2_2 = sum(event2_2),
            sum_event2_3 = sum(event2_3),
            sum_event2_4 = sum(event2_4),
            sum_event2_5 = sum(event2_5),
            sum_event2_6 = sum(event2_6),
            sum_event2_7 = sum(event2_7),
            sum_event2_8 = sum(event2_8),
            sum_event2_9 = sum(event2_9),
            sum_event2_10 = sum(event2_10),
            avg_date_diff = mean(date_diff,na.rm = TRUE)
            )

head(df)
```

Another metric we can include is revenue per product for cumuative value as well as previous orders
```{r}
df$cumrev_per_prod_till_prev_order <- ifelse(df$cumrev_till_prev_order==0,0,df$cumrev_till_prev_order/df$cumnum_prod_till_prev_order)

df$rev_per_prod_prev_ord <- ifelse(df$rev_prev_ord==0,0,df$rev_prev_ord/df$num_prod_prev_ord)
df[,c('cumrev_till_prev_order','cumnum_prod_till_prev_order','rev_prev_ord','num_prod_prev_ord')]<-NULL
```


```{r}
df$avg_date_diff<-as.numeric(df$avg_date_diff)
```

Breaking down orderdate to month, quarter, day-of-week, week of the year and hour
```{r}
df$order_month<-format(df$orderdate,"%m")
df$order_week_of_year<-strftime(df$orderdate,format="%W")
library(lubridate)
df$order_qtr<-quarter(df$orderdate)
df$order_day_of_week<-weekdays(df$orderdate,abbreviate = TRUE)
df$order_hour_of_day<-format(df$orderdate,"%H")

# converting the above features to factors
df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')] <- lapply(df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')], factor)
```


We have created the folllowing features by manipulating and combining order and online data.
```{r}
head(df)
```

The summary of the data is
```{r}
summary(df)
```

###3. Feature Selection

Lets look at the correlation between cumrev_per_prod_till_prev_order and rev_per_prod_prev_ord.
```{r}

cor(df[,!names(df) %in% c("custno","ordno","orderdate","prodcat1","order_month","order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")])
```
This is a very high correlation.
```{r}
cor(df$rev_per_prod_prev_ord,df$cumrev_per_prod_till_prev_order)
```
Therefore, we will choose only one metric as a predictor, which is rev_per_prod_prev_ord.
```{r}
df$cumrev_per_prod_till_prev_order <- NULL
```

For categorical variables, we will perform the chi-square test of association. We will compare various columns derived from orderdate. 
```{r}
#"custno","ordno","orderdate","prodcat1","order_month",
chisq.test(df$order_month,df$order_qtr)
chisq.test(df$order_day_of_week,df$order_hour_of_day)
chisq.test(df$order_day_of_week,df$order_week_of_year)
```
since the p-value is < 2.2e-16 is less than the cut-off value of 0.05, we can reject the null hypothesis in favor of alternative hypothesis and conclude, that the variables are dependent to each other. Therefore, we will only consider one variable for moedeling, which is order_month and delete the rest.

```{r}
df[,c("order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")]<-NULL

#removing id columns
df[,c("custno","ordno","orderdate")]<-NULL
```
We have removed combination of highly correlated variables and highly associated variable. During the model building phase we will encounter some variables that are not significant predictors to the response variable. In those steps, we will still be performing feature selection by removing insignificant predictors and keeping significant ones.

##4. Model Designing and sampling

We have prepared the data that now we can use to fit a model. We are trying to fit a model which predicts what product category-1 is a user most likely to buy based on his past online-activity as well as his buying behaviour. We will split the data into training and test sample. We will use the training sample to fit different classification models and test sample to measure the performance of the model. The train-test split is 70-30 split, i.e., 70% of the data is used for training and 30% for testing.

```{r}
## 70% of the sample size
smp_size <- floor(0.70 * nrow(df))

## set the seed to make your partition reproducible
set.seed(1234)
train_ind <- sample(seq_len(nrow(df)), size = smp_size)

train <- df[train_ind, ]
test <- df[-train_ind, ]

```

Our response mode is prodcat1. We need to make sure that all the classes of prodcat1 are present in train and test samples
```{r}
table(train$prodcat1)
```

```{r}
table(test$prodcat1)
```

In the next section, we will use different modelling techniques to fit a multi-class classifcation models. We will use the following algorithms
*1. Logistic regression
*2. Random Forest Regression

Logistic regression works well for linear relationships and has high interpretability, whereas Random Forest can fit non-linear relationships at the cost of interpretation.

The metric we will use to determine the best model is test-AUC (Area under the curve of the ROC curve for test sample)

##5. Model Generation and Evaluation

```{r}
#remove unnecessary objects to free-up space
rm(list=ls()[! ls() %in% c("df","train","test","online","order")])
gc()
```

In this step we will fit different models on the training sample and predict for the test sample 

### Logistic Regrssion
We will fit a mutinomial logistic regression model. We will ignore num_days_till_last_order and avg_date_diff in logistic regression as they have NA values. We could impute those values but given the time constraint, we will choose to ignore them. 
```{r}
train1<- train
test1<- test
train1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
test1[,c("num_days_till_last_order","avg_date_diff")]<-NULL

library(nnet)
# Fit the model
glm <- nnet::multinom(prodcat1 ~., data = train1)
# Summarize the model
summary(glm)
```

Now we'll calculate Z score and p-Value for the variables in the model.
```{r}

z <- summary(glm)$coefficients/summary(glm)$standard.errors

p <- (1 - pnorm(abs(z), 0, 1))*2
p
```

Calculating the the odds ratio coefficient for each predictor 
```{r}
exp(coef(glm))
```

Calculate Variable importance (absolute value of t-statistic)
```{r}
varimp_glm<-as.data.frame(varImp(glm))
varimp_glm$predictor<-rownames(varimp_glm)
colnames(varimp_glm)[1]<-'importance'

varimp_glm %>% arrange(desc(importance))

```
We can see that order month is the most important parameter. This is evident from the time series trends that we observed while exploring the data. Other important variables were sum_event1_8 ,sum_event1_8, and sum_event1_5 

Let's check for fitted values now.
```{r}
head(fitted(glm))
```


predicting on the test data
```{r}
predict_tst=as.data.frame(predict(glm,test1,type="probs"))
colnames(predict_tst)<-sapply(colnames(predict_tst), function(x) paste('logit_',x,sep = ""))
predict_tst$predicted_class<-apply(predict_tst,1,which.max)
predict_tst$predicted_class<-ifelse(predict_tst$predicted_class==6,7,predict_tst$predicted_class)
head(predict_tst)

#test1=cbind(test1, predict_tst)
```

Creating confusion matrix for test sample
```{r}
tab<-table(predict_tst$predicted_class,test1$prodcat1)
library(caret) 
conf<-confusionMatrix(tab)
conf
```
Class2 has high sensitivity, which means the model has a higher True Positive Rate for Class2. This means that the model does a good job of predicting whether a customer will will buy product category 2. At the same time it does a poor job of predicting whether a customer is not going to buy a product from prodcat2 or not. This is evident from the specificity of Class2

If we  we look at the sensitivity and specificity across all the other classes, we will see that the sensitivity values are low and specificity values are high. This means that, for the other classes the model does a better job identifying whether a customer is not going to buy a product in that class than predicting whether a customer is going to buy a product in that class



Calculating Test AUC of the ROC curve. The AUC is a measure of how well a model does a job of distinguishing between classes 
```{r}
library(HandTill2001)
auc(multcap(response=test1$prodcat1,predicted = predict(glm,test1,type="probs")))
```
This is a decent value. But it could be improved further by using complex models.

### Random Forest Classification


```{r}
# train1<- train
# test1<- test
# train1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
# test1[,c("num_days_till_last_order","avg_date_diff")]<-NULL

library(randomForest)
# Fit the model
set.seed(1234)
rf <- randomForest(prodcat1 ~., data = train1, ntree=500, mtry=round(sqrt(ncol(train)-1)), importance=TRUE)
# Summarize the model
rf
```



Calculate Variable importance
```{r}
varImp(rf)
```
Similar to what we have observed in the multinomial logistic regression, we can see that order month is the most important predictor.


predicting on the test data
```{r}
predict_tst_rf=as.data.frame(predict(rf,test1,type="prob"))
colnames(predict_tst_rf)<-sapply(colnames(predict_tst_rf), function(x) paste('rf_',x,sep = ""))
predict_tst_rf$predicted_class_rf<-apply(predict_tst_rf,1,which.max)
predict_tst_rf$predicted_class_rf<-ifelse(predict_tst_rf$predicted_class_rf==6,7,predict_tst_rf$predicted_class_rf)
head(predict_tst_rf)

#test1=cbind(test1, predict_tst_rf)
```

Creating confusion matrix for test sample
```{r}
tab_rf<-table(predict_tst_rf$predicted_class_rf,test1$prodcat1)
library(caret) 
conf_rf<-confusionMatrix(tab_rf)
conf_rf
```
The accuracy of the model is similar to the multinomial logisitic regression. Even the sensitivity and specificity across the classes is similar to multinomial logistic regression. Class 2 has high sensitivity and low specificity and all the other classes have low sensitivity and high specificity. 


Calculating Test AUC of the ROC curve
```{r}
library(HandTill2001)
auc(multcap(response=test$prodcat1,predicted = predict(rf,test1,type="prob")))
```

The random forest model has better fit on the training data, as evident from the model summary, but it does not do a job better than multinomial logistic regression to seperate the classes. One possible reason could be that we did not choose that big of an ensemble. The number of trees that we choose in the forest were only 500. If we increase it, the performance will improve.


### Random Forest with hyper parameter tuning

We tune the hyperparameters of random forest model so that it can converge on a more optimal output. There are two hyper parameters of the random forest

*1. mtry: number of predictors randomly chosen for the decision trees in the forests
*2. ntree: total number of decision trees in the forest.

One caveat though, this process requires a lot of computation and takes some time to converge.
```{r}
levels(train1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
levels(test1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
```


```{r}
library(tidyverse)
library(caret)
library(randomForest)
customRF <- list(type = "Classification", library = "randomForest", loop = NULL)
customRF$parameters <- data.frame(parameter = c("mtry", "ntree"), class = rep("numeric", 2), label = c("mtry", "ntree"))
customRF$grid <- function(x, y, len = NULL, search = "grid") {}
customRF$fit <- function(x, y, wts, param, lev, last, weights, classProbs, ...) {
  randomForest(x, y, mtry = param$mtry, ntree=param$ntree, ...)
}
customRF$predict <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
  predict(modelFit, newdata)
customRF$prob <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
  predict(modelFit, newdata, type = "prob")
customRF$sort <- function(x) x[order(x[,1]),]
customRF$levels <- function(x) x$classes
```

```{r}
control <- trainControl(method="cv", number=10, #repeats=3, 
                        classProbs = TRUE)
tunegrid <- expand.grid(.mtry=c(15:18), .ntree=c(500, 1000))
set.seed(1234)
custom <- train(prodcat1~., data=train1, method=customRF, metric="ROC", tuneGrid=tunegrid, trControl=control)
summary(custom)
plot(custom)
```

I have included the code but has not run it as it takes a lot of time to run and knit the report.

##6. Summary

To summarise, we had the customer order data as well as customer online activity data. We explored the data and found out that there is a seasonality in the revenue, number of orders, as well as the online activity. It peaks during Nov and Dec and drops during the months of Feb and Oct. We also saw that this trend is consitent across browsing categories as well as differnet online events. We also found out that most of the online activity is done on browsing category 3.

We also tried associating customer order data with online behaviour. While doing so, we made an assumption  
*1. Only the last 30 days of online activity drives buying behaviour for a customer.  
Any activity before that does not affect buying behaviour significantly. Based on this assumption, we have merged the online data with the order data. We were also able to derive som metrics like, count of each online event before the purchase, Number of days since last order, order month etc. We have used this metric to predict product category-1.

The predictive problem we are trying to solve is: Based on historical purchases and online beviour, what is the likelihood that a customer would purchase a product from a product-category1. To fit and measure the performance of the model, we first split the data into training and test sample. 70% of the data is used for training and 30% for measure its performance on unseen data. We have tried multinomial logistic regression, random forest, and random forest with hyper parameter tuning. Both the models performed decent on the test data. The models are good at identifying whether a customer is not going to buy from a particular product-category. The AUC value shows that the model does a decent job of separating classes in logistic regression. To improve the performance of the random forest model, we can perform hyperparameter tuning using a grid-search approach. This process takes a lot of time and computation capacity. I have shared the code for doing that.

With a better predicitve power, we can predict with high accuracy the product category where a customer is mostly likely to shop from. We can use this information to run targeted campaign or provide incentive to buy back from us.